Algebraic Topology: An Introduction

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Algebraic Topology: An Introduction
William S. Massey, William S. ...
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Last edited by Drini
June 30, 2020 | History

Algebraic Topology: An Introduction

  • 2 Want to read
  • 1 Currently reading

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Language
English

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Previews available in: English

Edition Availability
Cover of: Algebraic Topology
Algebraic Topology: An Introduction (Graduate Texts in Mathematics)
January 8, 1990, Springer
in English
Cover of: Algebraic topology, an introduction
Algebraic topology, an introduction
1977, Springer-Verlag, Springer
in English - 4th corrected printing.
Cover of: Algebraic topology
Algebraic topology: an introduction
1967, Harcourt, Brace &World
in English
Cover of: Algebraic topology
Algebraic topology: an introduction
1967, Harcourt, Brace & World
in English
Cover of: Algebraic topology
Algebraic topology: an introduction
1967, Harcourt, Brace and World
Cover of: Algebraic topology
Algebraic topology: an introduction
1967, Harcourt
in English
Cover of: Algebraic topology
Cover of: Algebraic Topology: An Introduction
Algebraic Topology: An Introduction
Publisher unknown
in English

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Book Details


First Sentence

"This textbook is designed to introduce advanced undergraduate or beginning graduate students to algebraic topology as painlessly as possible."

Table of Contents

Preface
Page ix
Note to the Student
Page xiii
Contents
Page xvii
One. Two-Dimensional Manifolds
Page 1
1. Introduction
Page 1
2. Definition and examples of n-manifolds
Page 2
3. Orientable vs. nonorientable manifolds
Page 3
4. Examples of compact, connected 2-manifolds
Page 6
5. Statement of the classification theorem for compact surfaces
Page 10
6. Triangulation of compact surfaces
Page 15
7. Proof of Theorem 5.1
Page 18
8. The Euler characteristic of a surface
Page 29
9. Manifolds with Boundary
Page 35
10. The classification of compact, connected 2-manifolds with boundary
Page 37
11. The Euler characteristic of a bordered surface
Page 42
12. Models of compact bordered surfaces in Euclidean 3-space
Page 43
13. Remarks on noncompact surfaces
Page 47
Two. The Fundamental Group
Page 55
1. Introduction
Page 55
2. Basic Notation and Terminology
Page 56
3. Definition of the fundamental group of a space
Page 58
4. The effect of a continuous mapping on the fundamental group
Page 63
5. The fundamental group of a circle is infinite cyclic
Page 68
6. Application: The Brouwer fixed-point theorem in dimension 2
Page 74
7. The fundamental group of a product space
Page 76
8. Homotopy type and homotopy equivalence of spaces
Page 78
Three. Free Groups and Free Products of Groups
Page 85
1. Introduction
Page 85
2. The weak product of abelian groups
Page 85
3. Free abelian groups
Page 89
4. Free products of groups
Page 97
5. Free groups
Page 102
6. The presentation of groups be generators and relations
Page 105
7. Universal mapping problems
Page 108
Four. Seifert and Van Kampen Theorem on the Fundamental Group of the Union of Two Spaces. Applications
Page 113
1. Introduction
Page 113
2. Statement and proof of the theorem of Seifert and Van Kampen
Page 114
3. First application of Theorem 2.1
Page 122
4. Second application of Theorem 2.1
Page 127
5. Structure of the fundamental group of a compact surface
Page 129
6. Application to knot theory
Page 136
Five. Covering Spaces
Page 145
1. Introduction
Page 145
2. Definition and some examples of covering spaces
Page 145
3. Lifting of paths to a covering space
Page 151
4. The fundamental group of a covering space
Page 154
5. Lifting of arbitrary maps to a covering space
Page 155
6. Homomorphisms and automorphisms of covering spaces
Page 158
7. The action of the group $pi(X,x)$ on the set $p^{-1}(x)$
Page 161
8. Regular covering spaces and quotient spaces
Page 164
9. Application: The Borsuk-Ulam theorem for the 2-sphere
Page 170
10. The existence theorem for covering spaces
Page 173
11. The induced covering space over a subspace
Page 177
12. Point set topology of covering spaces
Page 180
Six. The Fundamental Group and Covering Spaces of a Graph. Applications to Group Theory
Page 189
1. Introduction
Page 189
2. Definition and Examples
Page 190
3. Basic properties of graphs
Page 192
4. Trees
Page 194
5. The fundamental group of a graph
Page 197
6. The Euler characteristic of a finite graph
Page 200
7. Covering spaces of a graph
Page 201
8. Generators for a subgroup of free group
Page 204
Seven. The Fundamental Group of Higher Dimensional Spaces
Page 211
1. Introduction
Page 211
2. Adjunction of 2-cells to a space
Page 212
3. Adjunction of higher dimensional cells to a space
Page 214
4. CW-complexes
Page 215
5. The Kurosh subgroup theorem
Page 218
6. Grushko's theorem
Page 225
Eight. Epilogue
Page 236
Appendix A. The Quotient Space of Identification Space Topology
Page 243
1. Definition and basic properties
Page 243
2. A generalization of the quotient space topology
Page 246
3. Quotient spaces and product spaces
Page 249
4. Subspace of a quotient space vs. quotient space of a subspace
Page 250
5. Conditions for a quotient space to be a Hausdorff space
Page 251
Appendix B. Permutation Groups or Transformation Groups
Page 254
1. Basic definitions
Page 254
2. Homogeneous G-spaces
Page 256
Index
Page 259

Edition Notes

Series
Graduate Texts in Mathematics v. 56

ID Numbers

Open Library
OL23298394M
ISBN 10
0387902716
Goodreads
208763

First Sentence

"This textbook is designed to introduce advanced undergraduate or beginning graduate students to algebraic topology as painlessly as possible."

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History

Download catalog record: RDF / JSON / OPDS | Wikipedia citation
June 30, 2020 Edited by Drini Merge works
August 18, 2010 Edited by WorkBot merge works
April 16, 2010 Edited by bgimpertBot Added goodreads ID.
December 15, 2009 Edited by WorkBot link works
May 30, 2009 Created by netrapture add TOC