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Geometry and Topology of Configuration Spaces

  • Edward R. Fadell
  • Sufian Y. Husseini

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

Table of contents

  1. Front Matter
    Pages i-xvi
  2. The Homotopy Theory of Configuration Spaces

    1. Front Matter
      Pages 1-1
    2. Edward R. Fadell, Sufian Y. Husseini
      Pages 3-4
    3. Edward R. Fadell, Sufian Y. Husseini
      Pages 5-12
    4. Edward R. Fadell, Sufian Y. Husseini
      Pages 13-28
    5. Edward R. Fadell, Sufian Y. Husseini
      Pages 29-55
    6. Edward R. Fadell, Sufian Y. Husseini
      Pages 57-90
  3. Homology and Cohomology of $$ {\Bbb F}$$ k (M)

    1. Front Matter
      Pages 91-91
    2. Edward R. Fadell, Sufian Y. Husseini
      Pages 93-94
    3. Edward R. Fadell, Sufian Y. Husseini
      Pages 95-115
    4. Edward R. Fadell, Sufian Y. Husseini
      Pages 117-151
    5. Edward R. Fadell, Sufian Y. Husseini
      Pages 153-163
  4. Homology and Cohomology of Loop Spaces

    1. Front Matter
      Pages 165-165
    2. Edward R. Fadell, Sufian Y. Husseini
      Pages 167-169
    3. Edward R. Fadell, Sufian Y. Husseini
      Pages 171-185
    4. Edward R. Fadell, Sufian Y. Husseini
      Pages 187-206
    5. Edward R. Fadell, Sufian Y. Husseini
      Pages 207-223
    6. Edward R. Fadell, Sufian Y. Husseini
      Pages 225-242
    7. Edward R. Fadell, Sufian Y. Husseini
      Pages 243-267
    8. Edward R. Fadell, Sufian Y. Husseini
      Pages 269-291
    9. Edward R. Fadell, Sufian Y. Husseini
      Pages 293-303
  5. Back Matter
    Pages 305-313

About this book

Introduction

The configuration space of a manifold provides the appropriate setting for problems not only in topology but also in other areas such as nonlinear analysis and algebra. With applications in mind, the aim of this monograph is to provide a coherent and thorough treatment of the configuration spaces of Eulidean spaces and spheres which makes the subject accessible to researchers and graduate students with a minimal background in classical homotopy theory and algebraic topology. The treatment regards the homotopy relations of Yang-Baxter type as being fundamental. It also includes a novel and geometric presentation of the classical pure braid group; the cellular structure of these configuration spaces which leads to a cellular model for the associated based and free loop spaces; the homology and cohomology of based and free loop spaces; and an illustration of how to apply the latter to the study of Hamiltonian systems of k-body type.

Keywords

Algebraic topology Homotopy Loop group cohomology fibrations homology homotopy theory

Authors and affiliations

  • Edward R. Fadell
    • 1
  • Sufian Y. Husseini
    • 1
  1. 1.Department of MathematicsUniversity of Wisconsin-MadisonMadisonUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-56446-8
  • Copyright Information Springer-Verlag Berlin Heidelberg 2001
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-63077-4
  • Online ISBN 978-3-642-56446-8
  • Series Print ISSN 1439-7382
  • Buy this book on publisher's site