Name: Manifolds and Local Structures: A General Theory (en Inglés)
Price: 199.86 USD
Availability: InStock
Author: Grandis, Marco
ISBN: 9789811233999

portada Manifolds and Local Structures: A General Theory (en Inglés)

Formato

Libro Físico

Autor

Marco Grandis

Editorial

World Scientific Publishing Company

Idioma

Inglés

N° páginas

376

Encuadernación

Tapa Dura

Dimensiones

22.9 x 15.2 x 2.2 cm

Peso

0.67 kg.

ISBN13

9789811233999

Categorías

Algebra
Geometría
Topología

Manifolds and Local Structures: A General Theory (en Inglés)

Marco Grandis (Autor) · World Scientific Publishing Company · Tapa Dura

Libro Físico

$ 199.86

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Origen: Estados Unidos (Costos de importación incluídos en el precio)

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Reseña del libro "Manifolds and Local Structures: A General Theory (en Inglés)"

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.