{"product_id":"manifolds-local-structures-general-theory-9789811233999-new","title":"Manifolds and Local Structures: A General Theory","description":"\u003cp\u003eLocal structures, like differentiable manifolds, fibre bundles, vector bundles and foliations, can be obtained by gluing together a family of suitable 'elementary spaces', by means of partial homeomorphisms that fix the gluing conditions and form a sort of 'intrinsic atlas', instead of the more usual system of charts living in an external framework.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eAn 'intrinsic manifold' is defined here as such an atlas, in a suitable category of elementary spaces: open euclidean spaces, or trivial bundles, or trivial vector bundles, and so on.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eThis uniform approach allows us to move from one basis to another: for instance, the elementary tangent bundle of an open Euclidean space is automatically extended to the tangent bundle of any differentiable manifold. The same holds for tensor calculus.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eTechnically, the goal of this book is to treat these structures as 'symmetric enriched categories' over a suitable basis, generally an ordered category of partial mappings.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eThis approach to gluing structures is related to Ehresmann's one, based on inductive pseudogroups and inductive categories. A second source was the theory of enriched categories and Lawvere's unusual view of interesting mathematical structures as categories enriched over a suitable basis.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51544383521058,"sku":"9789811233999-new","price":138.6,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789811233999.jpg?v=1776403042","url":"https:\/\/www.albakireads.com\/products\/manifolds-local-structures-general-theory-9789811233999-new","provider":"AlbakiReads","version":"1.0","type":"link"}