Topology and Geometry
By: Glen E. Bredon.
Series: Graduate texts in mathematics ;
Publisher: Springer-Verlag
Published: 1993
Place of publication: New York
Language: eng
Format: Hardcover
Number of pages: 557
ISBN-13: 9780387979267
Subjects: Algebraic topology.
Other titles: Topology & geometry.
Notes: Includes bibliographical references (p. 541-543) and indexes.
Table of contents: label: Preface
pagenum: v; label: Acknowledgements
pagenum: ix; label: Chapter 1
title: General Topology
pagenum: 1; label: 1.
title: Metric Spaces
pagenum: 1; label: 2.
title: Topological Spaces
pagenum: 3; label: 3.
title: Subspaces
pagenum: 8; label: 4.
title: Connectivity and Components
pagenum: 10; label: 5.
title: Separation Axioms
pagenum: 12; label: 6.
title: Nets (Moore-Smith Convergence)*
pagenum: 14; label: 7.
title: Compactness
pagenum: 18; label: 8.
title: Products
pagenum: 22; label: 9.
title: Metric Spaces Again
pagenum: 25; label: 10.
title: Existence of Real Valued Functions
pagenum: 29; label: 11.
title: Locally Compact Spaces
pagenum: 31; label: 12.
title: Paracompact Spaces
pagenum: 35; label: 13.
title: Quotient Spaces
pagenum: 39; label: 14.
title: Homotopy
pagenum: 44; label: 15.
title: Topological Groups
pagenum: 51; label: 16.
title: Convex Bodies
pagenum: 56; label: 17.
title: The Baire Category Theorem
pagenum: 57; label: Chapter II
title: Diferentiable Manifolds
pagenum: 63; label: 1.
title: The Implicit Function Theorem
pagenum: 63; label: 2.
title: Differentiable Manifolds
pagenum: 68; label: 3.
title: Local Coordinates
pagenum: 71; label: 4.
title: Induced Structures and Examples
pagenum: 72; label: 5.
title: Tangent Vectors and Differentials
pagenum: 76; label: 6.
title: Sard's Theorem and Regular Values
pagenum: 80; label: 7.
title: Local Properties of Immersions and Submersions
pagenum: 82; label: 8.
title: Vector Fields and Flows
pagenum: 86; label: 9.
title: Tangent Bundles
pagenum: 88; label: 10.
title: Embedding in Euclidean Space
pagenum: 89; label: 11.
title: Tubular Neighborhoods and Approximations
pagenum: 92; label: 12.
title: Classical Lie Groups*
pagenum: 101; label: 13.
title: Fiber Bundles*
pagenum: 106; label: 14.
title: Induced Bundles and Whitney Sums*
pagenum: 111; label: 15.
title: Transversality*
pagenum: 114; label: 16.
title: Thom-Pontryagin Theory*
pagenum: 118; label: Chapter III
title: Fundamental Group
pagenum: 127; label: 1.
title: Homotopy Groups
pagenum: 127; label: 2.
title: The Fundamental Group
pagenum: 132; label: 3.
title: Covering Spaces
pagenum: 138; label: 4.
title: The Lifting Theorem
pagenum: 143; label: 5.
title: The Action of π_1 on the Fiber
pagenum: 146; label: 6.
title: Deck Transformations
pagenum: 147; label: 7.
title: Properly Discontinuous Actions
pagenum: 150; label: 8.
title: Classification of Covering Spaces
pagenum: 154; label: 9.
title: The Seifert-Van Kampen Theorem*
pagenum: 158; label: 10.
title: Remarks on SO(3)*
pagenum: 164; label: Chapter IV
title: Homology Theory
pagenum: 168; label: 1.
title: Homology Groups
pagenum: 168; label: 2.
title: The Zeroth Homology Group
pagenum: 172; label: 3.
title: The First Homology Group
pagenum: 172; label: 4.
title: Functorial Properties
pagenum: 175; label: 5.
title: Homological Algebra
pagenum: 177; label: 6.
title: Axioms for Homology
pagenum: 182; label: 7.
title: Computation of Degrees
pagenum: 190; label: 8.
title: CW-Complexes
pagenum: 194; label: 9.
title: Conventions for CW-Complexes
pagenum: 198; label: 10.
title: Cellular Homology
pagenum: 200; label: 11.
title: Cellular Maps
pagenum: 207; label: 12.
title: Products of CW-Complexes*
pagenum: 211; label: 13.
title: Euler's Formula
pagenum: 215; label: 14.
title: Homology of Real Projective Space
pagenum: 217; label: 15.
title: Singular Homology
pagenum: 219; label: 16.
title: The Cross Product
pagenum: 220; label: 17.
title: Subdivision
pagenum: 223; label: 18.
title: The Mayer-Victoris Sequence
pagenum: 228; label: 19.
title: The Generalized Jordan Curve Theorem
pagenum: 230; label: 20.
title: The Borsuk-Ulam Theorem
pagenum: 240; label: 21.
title: Simplicial Complexes
pagenum: 245; label: 22.
title: Simplicial Maps
pagenum: 250; label: 23.
title: The Lefschetz-Hopf Fixed Point Theorem
pagenum: 253; label: Chapter V
title: Cohomology
pagenum: 260; label: 1.
title: Multilinear Algebra
pagenum: 260; label: 2.
title: Differential Forms
pagenum: 261; label: 3.
title: Integration of Forms
pagenum: 265; label: 4.
title: Stokes' Theorem
pagenum: 267; label: 5.
title: Relationship to Singular Homology
pagenum: 269; label: 6.
title: More Homological Algebra
pagenum: 271; label: 7.
title: Universal Coefficient Theorems
pagenum: 281; label: 8.
title: Excision and Homotopy
pagenum: 285; label: 9.
title: de Rham's Theorem
pagenum: 286; label: 10.
title: The de Rham Theory of CP^n*
pagenum: 292; label: 11.
title: Hopf's Theorem on Maps to Spheres*
pagenum: 297; label: 12.
title: Differential Forms on Compact Lie Groups*
pagenum: 304; label: Chapter VI
title: Products and Duality
pagenum: 315; label: 1.
title: The Cross Product and the Künneth Theorem
pagenum: 315; label: 2.
title: A Sign Convention
pagenum: 321; label: 3.
title: The Cohomology Cross Product
pagenum: 321; label: 4.
title: The Cup Product
pagenum: 326; label: 5.
title: The Cap Product
pagenum: 334; label: 6.
title: Classical Outlook on Duality*
pagenum: 338; label: 7.
title: The Orientation Bundle
pagenum: 340; label: 8.
title: Duality Theorems
pagenum: 348; label: 9.
title: Duality on Compact Manifolds with Boundary
pagenum: 355; label: 10.
title: Applications of Duality
pagenum: 359; label: 11.
title: Intersection Theory*
pagenum: 366; label: 12.
title: The Euler Class, Lefschetz Numbers, and Vector Fields*
pagenum: 378; label: 13.
title: The Gysin Sequence*
pagenum: 390; label: 14.
title: Lefschetz Coincidence Theory*
pagenum: 393; label: 15.
title: Steenrod Operations*
pagenum: 404; label: 16.
title: Construction of the Steenrod Squares*
pagenum: 412; label: 17.
title: Stiefel-Whitney Classes*
pagenum: 420; label: 18.
title: Plumbing*
pagenum: 426; label: Chapter VII
title: Homotopy Theory
pagenum: 430; label: 1.
title: Cofibrations
pagenum: 430; label: 2.
title: The Compact-Open Topology
pagenum: 437; label: 3.
title: H-Spaces, H-Groups, and H-Cogroups
pagenum: 441; label: 4.
title: Homotopy Groups
pagenum: 443; label: 5.
title: The Homotopy Sequence of a Pair
pagenum: 445; label: 6.
title: Fiber Spaces
pagenum: 450; label: 7.
title: Free Homotopy
pagenum: 457; label: 8.
title: Classical Groups and Associated Manifolds
pagenum: 463; label: 9.
title: The Homotopy Addition Theorem
pagenum: 469; label: 10.
title: The Hurewicz Theorem
pagenum: 475; label: 11.
title: The Whitehead Theorem
pagenum: 480; label: 12.
title: Eilenberg-Mac Lane Spaces
pagenum: 488; label: 13.
title: Obstruction Theory*
pagenum: 497; label: 14.
title: Obstruction Cochains and Vector Bundles*
pagenum: 511; title: Appendices; label: App. A
title: The Additivity Axiom
pagenum: 519; label: App. B
title: Background in Set Theory
pagenum: 522; label: App. C
title: Critical Values
pagenum: 531; label: App. D
title: Direct Limits
pagenum: 534; label: App. E
title: Euclidean Neighbouhood Retracts
pagenum: 536; label: Bibliography
pagenum: 541; label: Index of Symbols
pagenum: 545; label: Index
pagenum: 549