Combinatorial Algebraic Topology
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Beschreibung
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 topology. Readers will probably find particularly useful the second part, which contains an in-depth discussion of the major research techniques of combinatorial algebraic topology. Our presentation of standard topics is quite different from that of existing texts. In addition, several new themes, such as spectral sequences, are included. 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.
The main benefit for the reader will be the prospect of fairly quickly getting to the forefront of modern research in this active field.
Includes supplementary material: sn.pub/extras
Autor*in
Dimitry Kozlov
Themen in »Combinatorial Algebraic Topology«
Characteristic class Homotopy cofibration combinatorics discrete mathematics fibrations graphs homology
Stimmen zu »Combinatorial Algebraic Topology«
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)
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