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Combinatorial Algebraic Topology

  • Dmitry Kozlov

Part of the Algorithms and Computation in Mathematics book series (AACIM, volume 21)

Table of contents

  1. Front Matter
    Pages I-XIX
  2. Concepts of Algebraic Topology

  3. Methods of Combinatorial Algebraic Topology

  4. Complexes of Graph Homomorphisms

  5. Back Matter
    Pages 377-389

About this book

Introduction

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, including Stiefel-Whitney characteristic classes, which are needed for the later parts. 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. 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.

Keywords

Algebraic topology Characteristic class Homotopy cofibration combinatorics discrete mathematics fibrations graphs homology

Authors and affiliations

  • Dmitry Kozlov
    • 1
  1. 1.Fachbereich 3 - MathematikUniversity of BremenBremenGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-71962-5
  • Copyright Information Springer-Verlag Berlin Heidelberg 2008
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-71961-8
  • Online ISBN 978-3-540-71962-5
  • Series Print ISSN 1431-1550
  • Buy this book on publisher's site