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Combinatorial Algebraic Topology

BuchGebunden
390 Seiten
Englisch
Springererschienen am24.10.2007
Combinatorial algebraic topology is a fascinating and dynamic field at the crossroads of algebraic topology and discrete mathematics. The first part of the book constitutes a swift walk through the main tools of algebraic topology, including Stiefel-Whitney characteristic classes, which are needed for the later parts.mehr
Verfügbare Formate
BuchGebunden
EUR128,39
BuchKartoniert, Paperback
EUR90,94
E-BookPDF1 - PDF WatermarkE-Book
EUR90,94

Produkt

KlappentextCombinatorial algebraic topology is a fascinating and dynamic field at the crossroads of algebraic topology and discrete mathematics. The first part of the book constitutes a swift walk through the main tools of algebraic topology, including Stiefel-Whitney characteristic classes, which are needed for the later parts.
ZusammenfassungCombinatorial 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.
Details
ISBN/GTIN978-3-540-71961-8
ProduktartBuch
EinbandartGebunden
Verlag
Erscheinungsjahr2007
Erscheinungsdatum24.10.2007
ReiheAlgorithms and Computation in Mathematics
Seiten390 Seiten
SpracheEnglisch
Gewicht812 g
IllustrationenXX, 390 p. 115 illus.
Artikel-Nr.10810184

Inhalt/Kritik

Inhaltsverzeichnis
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.mehr
Kritik
From the reviews:



"This is an introduction to the beautiful world of combinatorial algebraic topology, describing the modern research tools and latest applications in this field. ... This could be used as material for a reading seminar on Chromatic numbers and the Kneser Conjecture, structural theory of morphism complexes, characteristic classes and chromatic numbers, applications of spectral sequence to Hom Complexes. ... an interesting book with large perspective in studying problems on the borderline between discrete mathematics and algebraic topology." (Corina Mohorianu, Zentralblatt MATH, Vol. 1130 (8), 2008)

"This monograph offers an introduction to combinatorial algebraic topology, an active field connecting algebraic topology with discrete mathematics and computer science. It is intended to be 'A book to teach from', providing a self-contained introduction that swiftly guides the reader to the forefront of modern research." (St. Haller, Monatshefte für Mathematik, Vol. 162 (3), March, 2011)mehr

Autor

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.
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