- 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。
目录
◎图书目录
Preface
1. Diffeology and Diffeological Spaces
2. Locality and Diffeologies
3. Diffeological Vector Spaces
4. Modeling Spaces, Manifolds, etc.
5. Homotopy of Diffeological Spaces
6. Cartan-De Rham Calculus
7. Diffeological Groups
8. Diffeological Fiber Bundles
9. Symplectic Diffeology
Solutions to Exercises
Afterword
Notation and Vocabulary
Index
Bibliography
作者简介
◎作者简介 帕特里克·伊格莱西亚斯-泽穆尔(Patrick Iglesias-Zemmour)是法国马赛数学研究所研究员,也是以色列希伯来大学的长期客座教授。他以辛几何和广义微分几何的研究而闻名。他所著的《广义微分几何》(Diffeology)是该领域全世界的**部教材。
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