代数拓扑(天元基金影印系列丛书)
分类: 图书,科学与自然,数学,代数、数论、组合理论,
品牌: 哈彻著
基本信息·出版社：清华大学出版社
·ISBN：730210588X
·条形码：9787302105886
·包装版本：1
·装帧：平装
·丛书名：天元基金影印系列丛书
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内容简介《代数拓扑》：This geometrically flavored introduction to algebraic topology has the dual goals of serving as a textbook for a standard graduate-level course and as a background reference for many additional topics that do not usually fit into such a course. The broad coverage includes both the homological and homotopical sides of the subject. Care has been taken to present a readable, self-contained exposition, with many examples and exercises, aimed at the student or the researcher from another area of mathematics seeing the subject for the first time. The four main chapters present the basic core material of algebraic topology: fundamental groups, homology, cohomology, and higher homotopy groups. Each chapter concludes with a generous selection of optional topics, accounting for nearly half the book altogether.
目录
PrefaceChapter 0 Some Underlying Geometric NotionsChapter 1 The Fundamental Group 1.1 Basic Constructions 1.2 Van Kampen's Theorem 1.3 Coverng Spaces Additional TopicsChapter 2 Homology 2.1 Simplicial and Singular Homology 2.2 Computaiions and Applicaltions 2.3 The Formal Viewpoint Additional TopicsChapter 3 Cohomology 3.1 Cohomology Groups 3.2 Cup Product 3.3 Poincare Duality Additional TopicsChapter 4 Homotopy Theory 4.1 Homotopy Groups 4.2 Elementary Methods of Calculation 4.3 Connections with Cohomology Additional Topics Appendox Bibliography Index
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