A basic course in algebraic topology代数拓扑基础课程
点此进入淘宝搜索页搜索分类: 图书,进口原版书,科学与技术 Science & Techology ,
作者： William S. Massey著
出 版 社：
出版时间： 1997-5-1字数：版次：页数： 428印刷时间： 1997/05/01开本： 16开印次：纸张： 胶版纸I S B N ： 9780387974309包装： 精装内容简介
This book is intended to serve as a textbook for a course in algebraic topology at the beginning graduate level. The main topics covered are the classification of compact 2-manifolds, the fundamental group, covering spaces, singular homology theory, and singular cohomology theory. These topics are developed systematically, avoiding all unecessary definitions, terminology, and technical machinery. Wherever possible, the geometric motivation behind the various concepts is emphasized. The text consists of material from the first five chapters of the author's earlier book, ALGEBRAIC TOPOLOGY: AN INTRODUCTION (GTM 56), together with almost all of the now out-of- print SINGULAR HOMOLOGY THEORY (GTM 70). The material from the earlier books has been carefully revised, corrected, and brought up to date.
目录
Preface
Notation and Terminology
CHAPTER I
Two-Dimensional Manifolds
1. Introduction
2. Definition and Examples of n-Manifolds
3. Orientable vs. Nonorientable Manifolds
4. Examples of Compact, Connected 2-Manifolds
5. Statement of the Classification Theorem for Compact Surfaces
6. Triangulations of Compact Surfaces
7. Proof of Theorem 5.1
8. The Euler Characteristic of a Surface
References
CHAPTER II
The Fundamental Group
1. Introduction
2. Basic Notation and Terminology
3. Definition of the Fundamental Group of a Space
4. The Effect of a Continuous Mapping on the Fundamental Group
5. The Fundamental Group of a Circle Is Infinite Cyclic
6. Application: The Brouwer Fixed-Point Theorem in Dimension 2
7. The Fundamental Group of a Product Space
8. Homotopy Type and Homotopy Equivalence of Spaces
References
CHAPTER III
Free Groups and Free Products of Groups
1. Introduction
2. The Weak Product of Abelian Groups
3. Free Abelian Groups
4. Free Products of Groups
5. Free Groups
6. The Presentation of Groups by Generators and Relations
7. Universal Mapping Problems
References
CHAPTER IV
Seifert and Van Kampen Theorem on the Fundamental Group
of the Union of Two Spaces. Applications
1. Introduction
2. Statement and Proof of the Theorem of Seifert and Van Kampen
3. First Application of Theorem 2.1
4. Second Application of Theorem 2.1
5. Structure of the Fundamental Group of a Compact Surface
6. Application to Knot Theory
7. Proof of Lemma 2.4
References
CHAPTER V
Covering Spaces
1. Introduction
2. Definition and Some Examples of Covering Spaces
3. Lifting of Paths to a Covering Space
4. The Fundamental Group of a Covering Space
5. Lifting of Arbitrary Maps to a Covering Space
6. Homomorphisms and Automorphisms of Covering Space
……
CHAPTER VI
CHAPTER VII
CHAPTER VIII
CHAPTER IX
CHAPTER X
CHAPTER XI
CHAPTER XII
CHAPTER XIII
CHAPTER XIV
CHAPTER XV
APPENDIX A
APPENDIX B
Index
