Combinatorial Foundation of Homology and Homotopy

Applications to Spaces, Diagrams, Transformation Groups, Compactifications, Differential Algebras, Algebraic Theories, Simplicial Objects, and Resolutions

  • Hans-Joachim Baues

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages I-XV
  2. Examples and Applications

    1. Front Matter
      Pages 1-2
    2. Hans-Joachim Baues
      Pages 99-126
  3. Combinatorial Homology and Homotopy

    1. Front Matter
      Pages 127-128
    2. Hans-Joachim Baues
      Pages 129-168
    3. Hans-Joachim Baues
      Pages 169-202
    4. Hans-Joachim Baues
      Pages 203-228
    5. Hans-Joachim Baues
      Pages 229-248
    6. Hans-Joachim Baues
      Pages 249-265
    7. Hans-Joachim Baues
      Pages 267-300
    8. Hans-Joachim Baues
      Pages 301-313
    9. Hans-Joachim Baues
      Pages 315-354
  4. Erratum

    1. Hans-Joachim Baues
      Pages 370-370
  5. Back Matter
    Pages 355-369

About this book


This book considers deep and classical results of homotopy theory like the homological Whitehead theorem, the Hurewicz theorem, the finiteness obstruction theorem of Wall, the theorems on Whitehead torsion and simple homotopy equivalences, and characterizes axiomatically the assumptions under which such results hold. This leads to a new combinatorial foundation of homology and homotopy. Numerous explicit examples and applications in various fields of topology and algebra are given.


Homology Homotopy Hurewicz theorem algebraic theory cofibration homotopy theory resolution simplicial object

Authors and affiliations

  • Hans-Joachim Baues
    • 1
  1. 1.Max-Planck-Institut für MathematikBonnGermany

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 1999
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-08447-8
  • Online ISBN 978-3-662-11338-7
  • Series Print ISSN 1439-7382
  • Buy this book on publisher's site