天元基金影印系列丛书 代数拓扑 英文版 作者：（美）哈彻（Hatcher，A.）著 出版时间： 2005年版 内容简介 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 Preface Chapter 0 Some Underlying Geometric Notions Chapter 1 The Fundamental Group 1.1 Basic Constructions 1.2 Van Kampen's Theorem 1.3 Coverng Spaces Additional Topics Chapter 2 Homology 2.1 Simplicial and Singular Homology 2.2 Computaiions and Applicaltions 2.3 The Formal Viewpoint Additional Topics Chapter 3 Cohomology 3.1 Cohomology Groups 3.2 Cup Product 3.3 Poincare Duality Additional Topics Chapter 4 Homotopy Theory 4.1 Homotopy Groups 4.2 Elementary Methods of Calculation 4.3 Connections with Cohomology Additional Topics Appendox Bibliography Index
