This book is designed to be an introduction to some of the basic ideas in the field of algebraic topology. In particular, it is devoted to the foundations and applications of homology theory. The only prerequisite for the student is a basic knowledge of abelian groups and point set topology. The essentials of singular homology are given in the first chapter, along with some of the most important applications. In this way the student can quickly see the importance of the material. The successive topics include attaching spaces, finite CW complexes, the Eilenberg-Steenrod axioms, cohomology products, manifolds, Poincare duality, and fixed point theory. Throughout the book the approach is as illustrative as possible, with numerous examples and diagrams. Extremes of generality are sacrificed when they are likely to obscure the essential concepts involved. The book is intended to be easily read by students as a textbook for a course or as a source for individual study. The second edition has been substantially revised. It includes a new chapter on covering spaces in addition to illuminating new exercises.
Author(s): James W. Vick
Series: Pure and applied mathematics; a series of monographs and textbooks
Edition: 1st
Publisher: Academic Press
Year: 1973
Language: English
Pages: 237
Homology Theory: An Introduction to Algebraic Topology......Page 4
Copyright Page......Page 5
Contents......Page 8
Preface......Page 10
Acknowledgments......Page 12
CHAPTER 1. SINGULAR HOMOLOGY THEORY......Page 16
CHAPTER 2. ATTACHING SPACES WITH MAPS......Page 55
CHAPTER 3. THE EILENBERG–STEENROD AXIOMS......Page 89
CHAPTER 4. PRODUCTS......Page 113
CHAPTER 5. MANIFOLDS AND POINCARÉ DUALITY......Page 139
CHAPTER 6. FIXED-POINT THEORY......Page 188
APPENDIX I......Page 216
APPENDIX II......Page 224
References......Page 234
Books and Notes......Page 236
Survey and Expository Articles......Page 242
Index......Page 248
Pure and Applied Mathematics......Page 254
