Combinatorial 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.

Includes supplementary material: sn.pub/extras

Autorentext

The author is recipient of Wallenberg Prize of the Swedish Mathematics Society (2003), Gustafsson Prize of the Goran Gustafsson Foundation (2004), and the European Prize in Combinatorics (2005) (see http://www.math.tu-berlin.de/EuroComb05/prize.html for further information). He works at the interface of Discrete Mathematics, Algebraic
Topology, and Theoretical Computer Science.

He has obtained his doctorate from the Royal Institute of Technology, Stockholm in 1996. After longer stays at the Mathematical Sciences Research Institute at Berkeley, the Massachusetts Institute of Technology, the Institute for Advanced Study at Princeton, the University of Washington, Seattle, and Bern University, he has been a Senior Lecturer at the Royal Institute of Technology, Stockholm, and an Assistant Professor at ETH Zurich. Currently he holds the Chair of Algebra and Geometry at the University of Bremen, Germany.

Inhalt
Concepts of Algebraic Topology.- Overture.- Cell Complexes.- Homology Groups.- Concepts of Category Theory.- Exact Sequences.- Homotopy.- Cofibrations.- Principal ?-Bundles and StiefelWhitney 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.