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Combinatorial Foundation of Homology and Homotopy

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

  • Book
  • © 1999

Overview

Authors:
  1. Hans-Joachim Baues

    1. Max-Planck-Institut für Mathematik, Bonn, Germany

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

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Table of contents (13 chapters)

  1. Front Matter

    Pages I-XV
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  2. Examples and Applications

    1. Front Matter

      Pages 1-2
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    2. Examples and Applications in Topological Categories

      • Hans-Joachim Baues
      Pages 3-50

    3. Examples and Applications in Algebraic Homotopy Theories

      • Hans-Joachim Baues
      Pages 51-69

    4. Applications and Examples in Delicate Homotopy Theories of Simplicial Objects

      • Hans-Joachim Baues
      Pages 71-97

    5. Resolutions in Model Categories

      • Hans-Joachim Baues
      Pages 99-126

  3. Combinatorial Homology and Homotopy

    1. Front Matter

      Pages 127-128
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    2. Theories of Coactions and Homology

      • Hans-Joachim Baues
      Pages 129-168

    3. Twisted Chain Complexes and Twisted Homology

      • Hans-Joachim Baues
      Pages 169-202

    4. Basic Concepts of Homotopy Theory

      • Hans-Joachim Baues
      Pages 203-228

    5. Complexes in Cofibration Categories

      • Hans-Joachim Baues
      Pages 229-248

    6. Homology of Complexes

      • Hans-Joachim Baues
      Pages 249-265

    7. Realization of Chain Maps

      • Hans-Joachim Baues
      Pages 267-300

    8. Finiteness Obstructions

      • Hans-Joachim Baues
      Pages 301-313

    9. Non-Reduced Complexes and Whitehead Torsion

      • Hans-Joachim Baues
      Pages 315-354

  4. Erratum

    1. Erratum

      • Hans-Joachim Baues
      Pages 370-370

  5. Back Matter

    Pages 355-369
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Keywords

About this book

In this book we consider 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 we characterize 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.

Authors and Affiliations

  • Max-Planck-Institut für Mathematik, Bonn, Germany

    Hans-Joachim Baues

Bibliographic Information

  • Book Title: Combinatorial Foundation of Homology and Homotopy

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

  • Authors: Hans-Joachim Baues

  • Series Title: Springer Monographs in Mathematics

  • DOI: https://doi.org/10.1007/978-3-662-11338-7

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1999

  • Hardcover ISBN: 978-3-540-64984-7Published: 27 November 1998

  • Softcover ISBN: 978-3-642-08447-8Published: 15 December 2010

  • eBook ISBN: 978-3-662-11338-7Published: 09 March 2013

  • Series ISSN: 1439-7382

  • Series E-ISSN: 2196-9922

  • Edition Number: 1

  • Number of Pages: XV, 365

  • Topics: Algebraic Topology, Algebraic Geometry, K-Theory

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