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