广义微分几何

1星价 ¥102.3 (8.6折)

2星价￥102.3 定价￥119.0

作者：(法)帕特里克·伊格莱西亚斯-泽穆尔(P

出版社：世界图书出版公司

本类榜单：自然科学

分类：自然科学 > 数学

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ISBN：9787519296087
装帧：一般胶版纸
册数：暂无
重量：暂无
开本：24cm
页数：26,529页
出版时间：2022-09-01
条形码：9787519296087 ; 978-7-5192-9608-7

本书特色

◎媒体推荐/名人推荐/读者推荐 Diffeology is a natural extension of differential geometry that covers a wide spectrum of objects, ranging from singular spaces of any kind to infinite dimensional spaces, and sometimes mixing the two. With its developments in higher homotopy theory, fiber bundles, modeling spaces, Cartan-de-Rham calculus, moment map and symplectic constructions, to begin with, diffeology spans a wide range of traditional fields, treating geometrical objects that are or are not manifolds on an equal footing in a common framework. This textbook establishes the foundations of the theory, and develops the main areas of application. These are illustrated by a series of examples, chosen explicitly because they are not covered by traditional differential geometry. The advantage of diffeology comes from the conjunction of two strong properties: first, diffeology is stable by all set-theoretic operations: sum, product, subset and quotient. It is said to be a complete and co-complete category. It is also Cartesian closed, the set of smooth maps having itself a natural diffeology. Second, and perhaps more importantly, diffeology even deals with non-Hausdorff quotient spaces in a non-trivial way, as is the case with irrational tori. This specific property becomes crucial for new constructions and is at the origin of the generalization of theorems that do not exist otherwise.

内容简介

本书作者是PatrickIglesias-Zemnour是法国马赛数学研究所研究员(2019年退休)，目前是以色列耶路撒冷希伯来大学常期的客座教授。主要从事辛几何和厂义流形的研究。2013年在美国数学会MathematicalSurveysandMonographs系列丛书**次发表了关于广义流形的系统研究的专著。《广义流形》是该学科的**本教科书，由美国数学协会出版，奠定了在理论物理中使用的微分几何主要领域的基础：可微性、卡坦微分学、同源和上同源、不同群、纤维束和连接等。书中还配有习题和解答有助于读者更好地学习。