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Algebraic Topology

By Hatcher, Allen

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Book Id: WPLBN0000695484
Format Type: PDF eBook
File Size: 3.36 MB
Reproduction Date: 2005
Full Text

Title: Algebraic Topology  
Author: Hatcher, Allen
Volume:
Language: English
Subject: Science., Mathematics, Logic
Collections:
Historic
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Publisher:

Citation

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Hatcher, A. (n.d.). Algebraic Topology. Retrieved from http://hawaiilibrary.net/


Description
Mathematics document containing theorems and formulas.

Excerpt
Excerpt: Homology; Simplicial and Singular Homology; ¥ Complexes; Simplicial Homology; Singular Homology; Homotopy Invariance; Exact Sequences and Excision; and The Equivalence of Simplicial and Singular Homology.

Table of Contents
Table of Contents Chapter 0. Some Underlying Geometric Notions . . . . . 1 Homotopy and Homotopy Type 1. Cell Complexes 5. Operations on Spaces 8. Two Criteria for Homotopy Equivalence 11. The Homotopy Extension Property 14. Chapter 1. The Fundamental Group . . . . . . . . . . . . . 21 1. Basic Constructions . . . . . . . . . . . . . . . . . . . . . . . 25 Paths and Homotopy 25. The Fundamental Group of the Circle 28. Induced Homomorphisms 34. 2. Van Kampen?s Theorem . . . . . . . . . . . . . . . . . . . . 39 Free Products of Groups 39. The van Kampen Theorem 41. Applications to Cell Complexes 49. 3. Covering Spaces . . . . . . . . . . . . . . . . . . . . . . . . . 55 Lifting Properties 59. The Classification of Covering Spaces 62. Deck Transformations and Group Actions 69. Additional Topics A. Graphs and Free Groups 81. B. K(G,1) Spaces and Graphs of Groups 86

 

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