{"title":"Topology - General","description":"\u003cp\u003eGeneral topology investigates the fundamental properties of spaces, focusing on continuous transformations, open and closed sets, compactness, and connectedness. This field provides the groundwork for much of mathematical analysis and abstract algebra by formalizing concepts of nearness and continuity beyond geometry. Readers interested in understanding the basic language and tools that underpin much of modern mathematics will find general topology crucial.\u003c\/p\u003e\u003cp\u003eTo refine your exploration, consider how general topology links with areas such as set theory, point-set topology, or algebraic topology. If your research or coursework emphasizes abstract spaces rather than geometric intuition, this is an ideal starting place. For more specialized approaches, browsing related mathematics categories can help connect core topological concepts to advanced topics and applications.\u003c\/p\u003e","products":[{"product_id":"piecewise-linear-structures-topological-manifolds-9789814733786-new","title":"Piecewise Linear Structures on Topological Manifolds","description":"The study of triangulations of topological spaces has always been at the root of geometric topology. Among the most studied triangulations are piecewise linear triangulations of high-dimensional topological manifolds. Their study culminated in the late 1960s-early 1970s in a complete classification in the work of Kirby and Siebenmann. It is this classification that we discuss in this book, including the celebrated Hauptvermutung and Triangulation Conjecture.The goal of this book is to provide a readable and well-organized exposition of the subject, which would be suitable for advanced graduate students in topology. An exposition like this is currently lacking.","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51543615602978,"sku":"9789814733786-new","price":98.88,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789814733786.jpg?v=1776386648"},{"product_id":"etale-cohomology-theo-rev-ed-9789814675086-new","title":"Etale Cohomology Theo (REV Ed)","description":"\u003cp\u003eEtale cohomology is an important branch in arithmetic geometry. This book covers the main materials in SGA 1, SGA 4, SGA 4 1\/2 and SGA 5 on etale cohomology theory, which includes decent theory, etale fundamental groups, Galois cohomology, etale cohomology, derived categories, base change theorems, duality, and ℓ-adic cohomology. The prerequisites for reading this book are basic algebraic geometry and advanced commutative algebra.\u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51543633133858,"sku":"9789814675086-new","price":236.09,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789814675086.jpg?v=1776387405"},{"product_id":"adex-theory-9789814656498-new","title":"Adex Theory","description":"\u003cp\u003eThis book shows how the ADE Coxeter graphs unify at least 20 different types of mathematical structures. These mathematical structures are of great utility in unified field theory, string theory, and other areas of physics.\u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51543637262626,"sku":"9789814656498-new","price":119.68,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789814656498.jpg?v=1776387606"},{"product_id":"new-ideas-low-dimensional-topology-9789814630610-new","title":"New Ideas in Low Dimensional Topology","description":"\u003cp\u003eThis book consists of a selection of articles devoted to new ideas and developments in low dimensional topology. Low dimensions refer to dimensions three and four for the topology of manifolds and their submanifolds. Thus we have papers related to both manifolds and to knotted submanifolds of dimension one in three (classical knot theory) and two in four (surfaces in four dimensional spaces). Some of the work involves virtual knot theory where the knots are abstractions of classical knots but can be represented by knots embedded in surfaces. This leads both to new interactions with classical topology and to new interactions with essential combinatorics.\u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51543648370978,"sku":"9789814630610-new","price":202.83,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789814630610.jpg?v=1776387970"},{"product_id":"topics-real-complex-singularities-9789814596039-new","title":"Topics on Real and Complex Singularities","description":"A phenomenon which appears in nature, or human behavior, can sometimes be explained by saying that a certain potential function is maximized, or minimized. For example, the Hamiltonian mechanics, soapy films, size of an atom, business management, etc. In mathematics, a point where a given function attains an extreme value is called a critical point, or a singular point. The purpose of singularity theory is to explore the properties of singular points of functions and mappings.This is a volume on the proceedings of the fourth Japanese-Australian Workshop on Real and Complex Singularities held in Kobe, Japan. It consists of 11 original articles on singularities. Readers will be introduced to some important new notions for characterizations of singularities and several interesting results are delivered. In addition, current approaches to classical topics and state-of-the-art effective computational methods of invariants of singularities are also presented. This volume will be useful not only to the singularity theory specialists but also to general mathematicians.","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51543660921122,"sku":"9789814596039-new","price":120.72,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789814596039.jpg?v=1776388452"},{"product_id":"introductory-topology-exercises-solutions-9789814583817-new","title":"Introductory Topology: Exercises and Solutions","description":"The book offers a good introduction to topology through solved exercises. It is mainly intended for undergraduate students. Most exercises are given with detailed solutions.","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51543662952738,"sku":"9789814583817-new","price":38.74,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789814583817.jpg?v=1776388504"},{"product_id":"convergence-foundations-topology-9789814571524-new","title":"Convergence Foundations of Topology","description":"\u003cp\u003e\u003cem\u003eIt is clear that the book, with its high level of scholarship, is a labour of love on the part of its authors, and it will no doubt make quite a dent in the right circles ... The mature reader, disposed to this way of redoing topology, will have a great time.\"\u003c\/em\u003e\u003c\/p\u003e\u003cp\u003e\u003cem\u003eMathematical Association of America\u003c\/em\u003e\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eThis textbook is an alternative to a classical introductory book in point-set topology. The approach, however, is radically different from the classical one. It is based on convergence rather than on open and closed sets.\u003c\/p\u003e\u003cp\u003eConvergence of filters is a natural generalization of the basic and well-known concept of convergence of sequences, so that convergence theory is more natural and intuitive to many, perhaps most, students than classical topology. On the other hand, the framework of convergence is easier, more powerful and far-reaching which highlights a need for a theory of convergence in various branches of analysis.\u003c\/p\u003e\u003cp\u003eConvergence theory for filters is gradually introduced and systematically developed. Topological spaces are presented as a special subclass of convergence spaces of particular interest, but a large part of the material usually developed in a topology textbook is treated in the larger realm of convergence spaces.\u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51543666065698,"sku":"9789814571524-new","price":82.29,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789814571524.jpg?v=1776388686"},{"product_id":"topology-applications-9789814407656-new","title":"Topology with Applications","description":"The principal aim of this book is to introduce topology and its many applications viewed within a framework that includes a consideration of compactness, completeness, continuity, filters, function spaces, grills, clusters and bunches, hyperspace topologies, initial and final structures, metric spaces, metrization, nets, proximal continuity, proximity spaces, separation axioms, and uniform spaces.This book provides a complete framework for the study of topology with a variety of applications in science and engineering that include camouflage filters, classification, digital image processing, forgery detection, Hausdorff raster spaces, image analysis, microscopy, paleontology, pattern recognition, population dynamics, stem cell biology, topological psychology, and visual merchandising.It is the first complete presentation on topology with applications considered in the context of proximity spaces, and the nearness and remoteness of sets of objects. A novel feature throughout this book is the use of near and far, discovered by F Riesz over 100 years ago. In addition, it is the first time that this form of topology is presented in the context of a number of new applications.","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51543685726498,"sku":"9789814407656-new","price":112.4,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789814407656.jpg?v=1776389532"},{"product_id":"topological-library-part-3-9789814401302-new","title":"Topological Library: Part 3","description":"The final volume of the three-volume edition, this book features classical papers on algebraic and differential topology published in the 1950s-1960s. The partition of these papers among the volumes is rather conditional. The original methods and constructions from these works are properly documented for the first time in this book. No existing book covers the beautiful ensemble of methods created in topology starting from approximately 1950. That is, from Serre's celebrated \"singular homologies of fiber spaces.\"","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51543690510626,"sku":"9789814401302-new","price":222.57,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789814401302.jpg?v=1776389673"},{"product_id":"knots-physics-fourth-edition-9789814383011-new","title":"Knots and Physics, Fourth Edition","description":"This invaluable book is an introduction to knot and link invariants as generalized amplitudes for a quasi-physical process. The demands of knot theory, coupled with a quantum-statistical framework, create a context that naturally and powerfully includes an extraordinary range of interrelated topics in topology and mathematical physics. The author takes a primarily combinatorial stance toward knot theory and its relations with these subjects. This stance has the advantage of providing direct access to the algebra and to the combinatorial topology, as well as physical ideas.The book is divided into two parts: Part I is a systematic course on knots and physics starting from the ground up, and Part II is a set of lectures on various topics related to Part I. Part II includes topics such as frictional properties of knots, relations with combinatorics, and knots in dynamical systems.In this new edition, an article on Virtual Knot Theory and Khovanov Homology has beed added.","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51543695098146,"sku":"9789814383011-new","price":97.88,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789814383011.jpg?v=1776389888"},{"product_id":"knots-physics-fourth-edition-9789814383004-new","title":"Knots and Physics, Fourth Edition","description":"This invaluable book is an introduction to knot and link invariants as generalized amplitudes for a quasi-physical process. The demands of knot theory, coupled with a quantum-statistical framework, create a context that naturally and powerfully includes an extraordinary range of interrelated topics in topology and mathematical physics. The author takes a primarily combinatorial stance toward knot theory and its relations with these subjects. This stance has the advantage of providing direct access to the algebra and to the combinatorial topology, as well as physical ideas.The book is divided into two parts: Part I is a systematic course on knots and physics starting from the ground up, and Part II is a set of lectures on various topics related to Part I. Part II includes topics such as frictional properties of knots, relations with combinatorics, and knots in dynamical systems.In this new edition, an article on Virtual Knot Theory and Khovanov Homology has beed added.","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51543695130914,"sku":"9789814383004-new","price":331.7,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789814383004.jpg?v=1776389888"},{"product_id":"excursion-diagrammatic-algebra-9789814374491-new","title":"An Excursion in Diagrammatic Algebra","description":"The aim of this book is to give as detailed a description as is possible of one of the most beautiful and complicated examples in low-dimensional topology. This example is a gateway to a new idea of higher dimensional algebra in which diagrams replace algebraic expressions and relationships between diagrams represent algebraic relations. The reader may examine the changes in the illustrations in a leisurely fashion; or with scrutiny, the reader will become familiar and develop a facility for these diagrammatic computations.The text describes the essential topological ideas through metaphors that are experienced in everyday life: shadows, the human form, the intersections between walls, and the creases in a shirt or a pair of trousers. Mathematically informed reader will benefit from the informal introduction of ideas. This volume will also appeal to scientifically literate individuals who appreciate mathematical beauty.","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51543695851810,"sku":"9789814374491-new","price":122.79,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789814374491.jpg?v=1776389903"},{"product_id":"introductory-lectures-knot-theory-9789814307994-new","title":"Introductory Lectures on Knot Theory","description":"This volume consists primarily of survey papers that evolved from the lectures given in the school portion of the meeting and selected papers from the conference.Knot theory is a very special topological subject: the classification of embeddings of a circle or collection of circles into three-dimensional space. This is a classical topological problem and a special case of the general placement problem: Understanding the embeddings of a space X in another space Y. There have been exciting new developments in the area of knot theory and 3-manifold topology in the last 25 years. From the Jones, Homflypt and Kauffman polynomials, quantum invariants of 3-manifolds, through, Vassiliev invariants, topological quantum field theories, to relations with gauge theory type invariants in 4-dimensional topology.More recently, Khovanov introduced link homology as a generalization of the Jones polynomial to homology of chain complexes and Ozsvath and Szabo developed Heegaard-Floer homology, that lifts the Alexander polynomial. These two significantly different theories are closely related and the dependencies are the object of intensive study. These ideas mark the beginning of a new era in knot theory that includes relationships with four-dimensional problems and the creation of new forms of algebraic topology relevant to knot theory. The theory of skein modules is an older development also having its roots in Jones discovery. Another significant and related development is the theory of virtual knots originated independently by Kauffman and by Goussarov Polyak and Viro in the '90s. All these topics and their relationships are the subject of the survey papers in this book.It is a remarkable fact that knot theory, while very special in its problematic form, involves ideas and techniques that involve and inform much of mathematics and theoretical physics. The subject has significant applications and relations with biology, physics, combinatorics, algebra and the theory of computation. The summer school on which this book is based contained excellent lectures on the many aspects of applications of knot theory. This book gives an in-depth survey of the state of the art of present day knot theory and its applications.","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51543738777890,"sku":"9789814307994-new","price":202.83,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789814307994.jpg?v=1776391025"},{"product_id":"european-women-mathematics-9789814277679-new","title":"European Women in Mathematics","description":"This volume offers a unique collection of outstanding contributions from renowned women mathematicians who met in Cambridge for a conference under the auspices of European Women in Mathematics (EWM). These contributions serve as excellent surveys of their subject areas, including symplectic topology, combinatorics and number theory.The volume moreover sheds light on prominent women mathematicians who worked in Cambridge in the late 19th and early 20th centuries by providing an insightful historical introduction at the beginning of the volume.The volume concludes with short contributions from women mathematicians from across Europe working in various areas of mathematics ranging from group theory to magnetic fields.","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51543793205538,"sku":"9789814277679-new","price":124.87,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789814277679.jpg?v=1776392290"},{"product_id":"mereon-matrix-everything-connected-through-knothing-9789813233553-new","title":"The Mereon Matrix: Everything Connected Through (K)Nothing","description":"\u003cp\u003eIn this richly illustrated book, the contributors describe the Mereon Matrix, its dynamic geometry and topology. Through the definition of eleven First Principles, it offers a new perspective on dynamic, whole and sustainable systems that may serve as a template information model. This template has been applied to a set of knowledge domains for verification purposes: pre-life-evolution, human molecular genetics and biological evolution, as well as one social application on classroom management.\u003c\/p\u003e\u003cp\u003eThe importance of the book comes in the following ways: \u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eThe dynamics of the geometry unites all Platonic and Kepler Solids into one united structure and creates 11 unique trefoil knots. Its topology is directly related to the dynamics of the polyhedra.\u003c\/li\u003e\n\u003cli\u003eThe Mereon Matrix is an approach to the unification of knowledge that relies on whole systems modelling. it is a framework charting the emergence of the Platonic and Kepler solids in a sequential, emergent growth process that describes a non-linear whole system, and includes a process of 'breathing' as well as multiplying ('birthing');\u003c\/li\u003e\n\u003cli\u003eThis dynamic\/kinematic structure provides insight and a new approach to General Systems Theory and non-linear science, evolving through a new approach to polyhedral geometry. A set of 11 First Principles is derived from the structure, topology and dynamics of the Mereon Matrix, which serve well as a template information model.\u003c\/li\u003e\n\u003cli\u003eThe Mereon Matrix is related to a large number of systems, physical, mathematical, and philosophical, and in linking these systems, provides access to new relationships among them by combining geometry with process thinking. The new perspective on systems is hypothesized as universal -- this is, applicable in all areas of science, natural and social. Such applicability has been demonstrated for applications as diverse as pre-life evolution, biological evolution and human molecular genetics, as well as a classroom management system for the educational system.\u003c\/li\u003e\n\u003cli\u003eCare has been taken to use images and languaging that are understandable across domains, connecting diverse disciplines, while making this complex system easily accessible.\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51543898587426,"sku":"9789813233553-new","price":348.33,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789813233553.jpg?v=1776393904"},{"product_id":"geometry-topology-physics-moduli-spaces-higgs-bundles-9789813229082-new","title":"Geometry, Topology \u0026 Physics Moduli Spaces Higgs Bundles","description":"\u003cp\u003eIn the 25 years since their introduction, Higgs bundles have seen a surprising number of interactions within different areas of mathematics and physics. 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Our book contains material dating from the origins of the theory of foliations, from the original works of C Ehresmann and G Reeb, up till modern developments.\u003c\/p\u003e\u003cp\u003eIn a suitable choice of topics we are able to cover material in a coherent way bringing the reader to the heart of recent results in the field. A number of theorems, nowadays considered to be classical, like the Reeb Stability Theorem, Haefliger's Theorem, and Novikov Compact leaf Theorem, are proved in the text. The stability theorem of Thurston and the compact leaf theorem of Plante are also thoroughly proved. Nevertheless, these notes are introductory and cover only a minor part of the basic aspects of the rich theory of foliations.\u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51543944036642,"sku":"9789813207073-new","price":103.05,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789813207073.jpg?v=1776395345"},{"product_id":"introductory-topology-2nd-ed-9789813148024-new","title":"Introductory Topology: Exercises and Solutions (Second Edition)","description":"\u003cp\u003e\u003cem\u003e\"With the publication of the second edition, the author has made a good book even better. The author's writing style is clear and detailed, and therefore this book should be accessible to most reasonably well-prepared college students. The exercises come in a variety of forms. Most exercises have solutions appearing in the back of the book, but in every chapter there is a section of exercises for which there are no solutions, another factor which would help make this book suitable as a stand-alone text. To summarize: this is a valuable book. Any professor teaching a course in topology should have a copy close at hand.\"\u003c\/em\u003e\u003c\/p\u003e\u003cp\u003e\u003cem\u003eDr Mark Hunacek\u003cbr\u003e Iowa State University\u003c\/em\u003e\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003e\u003cstrong\u003e\u003cem\u003eReview of the First Edition: \u003c\/em\u003e\u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003e\u003cem\u003e\"The idea of numerous true-false questions was a particularly good one. 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These are presented in Part VII in the form of a sequence of chapters, many of which can be read or studied independently or in short sequences of two or three chapters, provided that the student has mastered the previous sections.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eChapters related to the more basic ideas of general topology are followed by a collection of 'concept review' questions, the answers to which are found in the main body of the text. These questions highlight the main concepts presented in that chapter, as well as ideas that are often overlooked when first encountered, which will help to test the students' understanding. The efforts required in answering correctly such questions will provide the student with the ability to solve more complex problems in the exercises collected at the end of each section.\u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51544125833506,"sku":"9789811277337-new","price":196.61,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789811277337.jpg?v=1776399125"},{"product_id":"invariants-pictures-9789811220111-new","title":"Invariants and Pictures","description":"\u003cp\u003eThis book contains an in-depth overview of the current state of the recently emerged and rapidly growing theory of \u003cem\u003eGnk\u003c\/em\u003e groups, picture-valued invariants, and braids for arbitrary manifolds. Equivalence relations arising in low-dimensional topology and combinatorial group theory inevitably lead to the study of invariants, and good invariants should be strong and apparent. An interesting case of such invariants is picture-valued invariants, whose values are not algebraic objects, but geometrical constructions, like graphs or polyhedra.\u003c\/p\u003e\u003cp\u003eIn 2015, V O Manturov defined a two-parametric family of groups \u003cem\u003eGnk\u003c\/em\u003e and formulated the following principle: if dynamical systems describing a motion of n particles possess a nice codimension 1 property governed by exactly k particles then these dynamical systems possess topological invariants valued in \u003cem\u003eGnk\u003c\/em\u003e.\u003c\/p\u003e\u003cp\u003eThe book is devoted to various realisations and generalisations of this principle in the broad sense. The groups \u003cem\u003eGnk\u003c\/em\u003e have many epimorphisms onto free products of cyclic groups; hence, invariants constructed from them are powerful enough and easy to compare. However, this construction does not work when we try to deal with points on a 2-surface, since there may be infinitely many geodesics passing through two points. That leads to the notion of another family of groups -- \u003cem\u003eΓnk\u003c\/em\u003e, which give rise to braids on arbitrary manifolds yielding invariants of arbitrary manifolds.\u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51544447254818,"sku":"9789811220111-new","price":123.85,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789811220111.jpg?v=1776404048"},{"product_id":"polynomial-one-cocycles-knots-closed-braids-9789811210297-new","title":"Polynomial One-Cocycles for Knots and Closed Braids","description":"\u003cp\u003eTraditionally, knot theory deals with diagrams of knots and the search of invariants of diagrams which are invariant under the well known Reidemeister moves. This book goes one step beyond: it gives a method to construct invariants for one parameter famillies of diagrams and which are invariant under \"higher\" Reidemeister moves. Luckily, knots in 3-space, often called classical knots, can be transformed into knots in the solid torus without loss of information. It turns out that knots in the solid torus have a particular rich topological moduli space. It contains many \"canonical\" loops to which the invariants for one parameter families can be applied, in order to get a new sort of invariants for classical knots.\u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51544479498530,"sku":"9789811210297-new","price":103.05,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789811210297.jpg?v=1776404849"},{"product_id":"quantum-invariants-v29-9789810246754-new","title":"Quantum Invariants (V29)","description":"This book provides an extensive and self-contained presentation of quantum and related invariants of knots and 3-manifolds. Polynomial invariants of knots, such as the Jones and Alexander polynomials, are constructed as quantum invariants, i.e. invariants derived from representations of quantum groups and from the monodromy of solutions to the Knizhnik-Zamolodchikov equation. With the introduction of the Kontsevich invariant and the theory of Vassiliev invariants, the quantum invariants become well-organized. Quantum and perturbative invariants, the LMO invariant, and finite type invariants of 3-manifolds are discussed. The Chern-Simons field theory and the Wess-Zumino-Witten model are described as the physical background of the invariants.","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51544502403362,"sku":"9789810246754-new","price":192.44,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789810246754.jpg?v=1776405696"},{"product_id":"abstract-homotopy-simple-homotopy-9789810216023-new","title":"Abstract Homotopy \u0026 Simple Homotopy the","description":"\u003cp\u003e \u003c\/p\u003e\u003cp\u003eThe abstract homotopy theory is based on the observation that analogues of much of the topological homotopy theory and simple homotopy theory exist in many other categories (e.g. spaces over a fixed base, groupoids, chain complexes, module categories). Studying categorical versions of homotopy structure, such as cylinders and path space constructions, enables not only a unified development of many examples of known homotopy theories but also reveals the inner working of the classical spatial theory. This demonstrates the logical interdependence of properties (in particular the existence of certain Kan fillers in associated cubical sets) and results (Puppe sequences, Vogt's Iemma, Dold's theorem on fibre homotopy equivalences, and homotopy coherence theory).\u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51544517476642,"sku":"9789810216023-new","price":134.24,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789810216023.jpg?v=1776406188"}],"url":"https:\/\/www.albakireads.com\/collections\/mathematics-topology-general.oembed","provider":"AlbakiReads","version":"1.0","type":"link"}