微分流形 罗格斯大学数学名誉教授 Differential Manifolds

基本信息

Series:Dover Books on Mathema 1.4tics

Format:Paperback / softback 288 pages

Publisher:Dover Publications Inc.

Imprint:Dover Publications Inc.

ISBN:9780486462448

Published:28 Dec 2007

Weight:306g

Dimensions:217 x 137 x 15 (mm)

页面参数仅供参考，具体以实物为准

书籍简介

微分拓扑的概念是许多数学学科的核心，例如微分几何和李群理论。《微分流形》向高年级本科生和研究生介绍了光滑流形拓扑结构的系统研究。作者安东尼·A·科辛斯基是罗格斯大学数学名誉教授，他提供了一种通俗易懂的方法，既可以解决 h 配边定理的问题，也可以解决球面上微分结构的分类问题。

《美国数学学会公报》指出，“有一本简短、写得很好的关于微分拓扑的书真是太有用了。”本书以对微分拓扑基础的详细、独立的回顾开始，只需要对初等代数拓扑有低限度的了解。后续章节解释了沿子流形连接流形的技术、手柄表示定理以及基于这些构造的 h 配边定理的证明。接下来的一章是关于庞特里亚金构造的，这是微分拓扑和同伦理论之间的主要联系。后面一章介绍了手术方法，并将其应用于球面光滑结构的分类。正文补充了许多有趣的历史注释，并包含一个新的附录，即约翰·W·摩根 (John W. Morgan) 撰写的《格里高利·佩雷尔曼的作品》，其中讨论了微分拓扑的新发展。

The concepts of differential topology form the center of many mathematical disciplines such as differential geometry and Lie group theory. Differential Manifolds presents to advanced undergraduates and graduate students the systematic study of the topological structure of smooth manifolds. Author Antoni A. Kosinski, Professor Emeritus of Mathematics at Rutgers University, offers an accessible approach to both the h-cobordism theorem and the classification of differential structures on spheres.

"How useful it is," noted the Bulletin of the American Mathematical Society, "to have a single, short, well-written book on differential topology." This volume begins with a detailed, self-contained review of the foundations of differential topology that requires only a minimal knowledge of elementary algebraic topology. Subsequent chapters explain the technique of joining manifolds along submanifolds, the handle presentation theorem, and the proof of the h-cobordism theorem based on these constructions. There follows a chapter on the Pontriagin Construction—the principal link between differential topology and homotopy theory. The final chapter introduces the method of surgery and applies it to the classification of smooth structures of spheres. The text is supplemented by numerous interesting historical notes and contains a new appendix, "The Work of Grigory Perelman," by John W. Morgan, which discusses the most recent developments in differential topology.

作者简介

安东尼·A·科辛斯基是罗格斯大学数学名誉教授。

Antoni A. Kosinski is Professor Emeritus of Mathematics at Rutgers University.