Symplectic Geometry & Mirror Symmetry
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Book Overview In 1993, M Kontsevich proposed a conceptual framework for explaining the phenomenon of mirror symmetry. Mirror symmetry had been discove...
In 1993, M Kontsevich proposed a conceptual framework for explaining the phenomenon of mirror symmetry. Mirror symmetry had been discovered by physicists in string theory as a duality between families of three-dimensional Calabi-Yau manifolds. Kontsevich's proposal uses Fukaya's construction of the A∞-category of Lagrangian submanifolds on the symplectic side and the derived category of coherent sheaves on the complex side. The theory of mirror symmetry was further enhanced by physicists in the language of D-branes and also by Strominger-Yau-Zaslow in the geometric set-up of (special) Lagrangian torus fibrations. It rapidly expanded its scope across from geometry, topology, algebra to physics.
In this volume, leading experts in the field explore recent developments in relation to homological mirror symmetry, Floer theory, D-branes and Gromov-Witten invariants. Kontsevich-Soibelman describe their solution to the mirror conjecture on the abelian variety based on the deformation theory of A∞-categories, and Ohta describes recent work on the Lagrangian intersection Floer theory by Fukaya-Oh-Ohta-Ono which takes an important step towards a rigorous construction of the A∞-category. There follow a number of contributions on the homological mirror symmetry, D-branes and the Gromov-Witten invariants, e.g. Getzler shows how the Toda conjecture follows from recent work of Givental, Okounkov and Pandharipande. This volume provides a timely presentation of the important developments of recent years in this rapidly growing field.
Book Details Format: Hardcover | Pages: 498 | Language: English | Publisher: WORLD SCIENTIFIC PUB CO INC | ISBN: 9810247141
FormatHardcover
Pages498
LanguageEnglish
ISBN9810247141
EAN9789810247140
PublisherWORLD SCIENTIFIC PUB CO INC
Publication Date2001-01-01
EditionFirst Edition
AccessoriesNo Accessory
ConditionNew
Product TypeHARD COVER BOOKS
Weight1.7 Pounds
Length8.6 Inches
Width6.2 Inches
Height1.2 Inches
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