Algebraic Topology: An Introduction (Graduate Texts in Mathematics) (v. 56)

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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!!!. 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 file:///C|/Documents and Settings/me/デスクトップ/desktop/pictures/getpedia.html......Page 1