Combinatorial Algebraic Topology

Authors:

ISBN: 978-3-540-71961-8 (Print) 978-3-540-71962-5 (Online)

Table of contents (20 chapters)

  1. Front Matter

    Pages I-XIX

  2. Concepts of Algebraic Topology

    1. No Access

      Book Chapter

      Pages 1-4

      Overture

    2. No Access

      Book Chapter

      Pages 7-35

      Cell Complexes

    3. No Access

      Book Chapter

      Pages 37-58

      Homology Groups

    4. No Access

      Book Chapter

      Pages 59-75

      Concepts of Category Theory

    5. No Access

      Book Chapter

      Pages 77-87

      Exact Sequences

    6. No Access

      Book Chapter

      Pages 89-100

      Homotopy

    7. No Access

      Book Chapter

      Pages 101-110

      Cofibrations

    8. No Access

      Book Chapter

      Pages 111-125

      Principal Γ-Bundles and Stiefel—Whitney Characteristic Classes

  3. Methods of Combinatorial Algebraic Topology

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      Book Chapter

      Pages 129-149

      Combinatorial Complexes Melange

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      Book Chapter

      Pages 151-178

      Acyclic Categories

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      Book Chapter

      Pages 179-209

      Discrete Morse Theory

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      Book Chapter

      Pages 211-224

      Lexicographic Shellability

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      Book Chapter

      Pages 225-243

      Evasiveness and Closure Operators

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      Book Chapter

      Pages 245-257

      Colimits and Quotients

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      Book Chapter

      Pages 259-273

      Homotopy Colimits

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      Book Chapter

      Pages 275-289

      Spectral Sequences

  4. Complexes of Graph Homomorphisms

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      Book Chapter

      Pages 293-308

      Chromatic Numbers and the Kneser Conjecture

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      Book Chapter

      Pages 309-326

      Structural Theory of Morphism Complexes

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      Book Chapter

      Pages 327-347

      Using Characteristic Classes to Design Tests for Chromatic Numbers of Graphs

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      Book Chapter

      Pages 349-376

      Applications of Spectral Sequences to Hom Complexes

  5. Back Matter

    Pages 377-389