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An introduction to algebraic topology

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This book is a clear exposition, with exercises, of the basic ideas of algebraic topology: homology (singular, simplicial, and cellular), homotopy groups, and cohomology rings. It is suitable for a two-semester course at the beginning graduate level, requiring as a prerequisite a knowledge of point set topology and basic algebra. Although categories and functors are introduced early in the text, excessive generality is avoided, and the author explains the geometric or analytic origins of abstract concepts as they are introduced, making this book of great value to the student.

Author(s): Joseph J. Rotman
Series: Graduate Texts in Mathematics
Publisher: Springer
Year: 1988

Language: English
Pages: 415

0 Introduction......Page 1
1 Some Basic Topological Notions......Page 14
2 Simplexes......Page 31
3 The Fundamental Group......Page 39
4 Singular Homology......Page 57
5 Long Exact Sequences......Page 86
6 Excision and Applications......Page 106
7 Simplicial Complexes......Page 131
8 CW Complexes......Page 180
9 Natural Transformations......Page 228
10 Covering Spaces......Page 272
11 Homotopy Groups......Page 310
12 Cohomology......Page 369