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Manifolds And Local Structures: A General Theory by Marco Grandis (Univ Di Genova, Italy) at Abbey's Bookshop,
Manifolds And Local Structures: A General Theory
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Marco Grandis (Univ Di Genova, Italy)

Manifolds And Local Structures

A General Theory

Marco Grandis (Univ Di Genova, Italy)

$230.99

Hardback

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English
World Scientific Publishing Co Pte Ltd
10 February 2021
Euclidean geometry
Local 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.

An '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.

This 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.

Technically, 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.

This 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.
By:  
Imprint:   World Scientific Publishing Co Pte Ltd
Country of Publication:   Singapore
ISBN:   9789811233999
ISBN 10:   9811233993
Pages:   376
Publication Date:  
Audience:   College/higher education ,  Professional and scholarly ,  Primary ,  Undergraduate
Format:   Hardback
Publisher's Status:   Active

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