Combinatorial Algebraic Topology

• Main Author: Kozlov, Dmitry (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2008.
• Series: Algorithms and Computation in Mathematics, 21
• Subjects: Mathematics.; Algebraic topology.; Combinatorics.; Algebraic Topology.

Combinatorial algebraic topology is a fascinating and dynamic field at the crossroads of algebraic topology and discrete mathematics. This volume is the first comprehensive treatment of the subject in book form. The first part of the book constitutes a swift walk through the main tools of algebraic...

Table of Contents:

• Concepts of Algebraic Topology
• Overture
• Cell Complexes
• Homology Groups
• Concepts of Category Theory
• Exact Sequences
• Homotopy
• Cofibrations
• Principal ?-Bundles and Stiefel—Whitney Characteristic Classes
• Methods of Combinatorial Algebraic Topology
• Combinatorial Complexes Melange
• Acyclic Categories
• Discrete Morse Theory
• Lexicographic Shellability
• Evasiveness and Closure Operators
• Colimits and Quotients
• Homotopy Colimits
• Spectral Sequences
• Complexes of Graph Homomorphisms
• Chromatic Numbers and the Kneser Conjecture
• Structural Theory of Morphism Complexes
• Using Characteristic Classes to Design Tests for Chromatic Numbers of Graphs
• Applications of Spectral Sequences to Hom Complexes.