This is a charming book on algebraic topology.It doesnt teach homology or cohomology theory,still you can find in it:about the fundamental group, the action of the fundamental group on the universal cover (and the concept of the universal cover),the classification of surfaces and a beautifull chapter on free groups and the way it is related to Van-kampen theorem .After reading this book you will have a strong intuitive picture on "what is algebraic topology all about"(well at list on part of algebraic topology)read it an enjoy it!!!.
Author(s): William S. Massey
Series: Graduate Texts in Mathematics v. 56
Publisher: Springer
Year: 1977
Language: English
Pages: 554
Title Page......Page 2
Table of Contents......Page 3
Preface......Page 6
Standard Notations......Page 9
Homotopy and Homotopy Type......Page 10
Cell Complexes......Page 14
Operations on Spaces......Page 17
Two Criteria for Homotopy Equivalence......Page 20
The Homotopy Extension Property......Page 23
1. The Fundamental Group......Page 30
Paths and Homotopy......Page 34
The Fundamental Group of the Circle......Page 37
Induces Homomorphisms......Page 43
Free Products of Groups......Page 48
The van Kampen Theorem......Page 50
Applications to Cell Complexes......Page 58
1.3 Covering Spaces......Page 64
Lifting Properties......Page 68
The Classification of Covering Spaces......Page 71
Deck Transformations and Group Actions......Page 78
1.A Graphs and Free Groups......Page 90
1.B K(G,1) Spaces and Graphs of Groups......Page 95
2. Homology......Page 106
Δ-Complexes......Page 111
Simplicial Homology......Page 113
Singular Homology......Page 116
Homotopy Invariance......Page 119
Exact Sequences, Relative Homology, and Exicision......Page 122
The Equivalence of Simplicial and Singular Homology......Page 137
2.2 Computations and Applications......Page 143
Local Disk......Page
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