Dimitry Kozlov

Combinatorial Algebraic Topology (eBook, PDF)

• Format: PDF

Produktbeschreibung

This volume is the first comprehensive treatment of combinatorial algebraic topology in book form. The first part of the book constitutes a swift walk through the main tools of algebraic topology. Readers - graduate students and working mathematicians alike - will probably find particularly useful the second part, which contains an in-depth discussion of the major research techniques of combinatorial algebraic topology. Although applications are sprinkled throughout the second part, they are principal focus of the third part, which is entirely devoted to developing the topological structure theory for graph homomorphisms.

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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 390
• Erscheinungstermin: 29. Dezember 2007
• Englisch
• ISBN-13: 9783540719625
• Artikelnr.: 44222092

Autorenporträt

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.

Inhaltsangabe

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.

Rezensionen

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)