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Geometry and Topology of Configuration Spaces

  • Book
  • © 2001

Overview

Authors:
  1. Edward R. Fadell

    1. Department of Mathematics, University of Wisconsin-Madison, Madison, USA

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  2. Sufian Y. Husseini

    1. Department of Mathematics, University of Wisconsin-Madison, Madison, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • Self-contained treatment of the topology of configuration spaces
  • Distinctive feature: it is more geometric than is traditional
  • More accessible account by the present authors as well as a consolidation of many results
  • Includes supplementary material: sn.pub/extras

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

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Table of contents (17 chapters)

  1. Front Matter

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

    1. Front Matter

      Pages 1-1
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    2. Introduction

      • Edward R. Fadell, Sufian Y. Husseini
      Pages 3-4

    3. Basic Fibrations

      • Edward R. Fadell, Sufian Y. Husseini
      Pages 5-12

    4. Configuration Space of ℝn+1, n > 1

      • Edward R. Fadell, Sufian Y. Husseini
      Pages 13-28

    5. Configuration Spaces of S n+1, n > 1

      • Edward R. Fadell, Sufian Y. Husseini
      Pages 29-55

    6. The Two Dimensional Case

      • Edward R. Fadell, Sufian Y. Husseini
      Pages 57-90

  3. Homology and Cohomology of $$ {\Bbb F}$$ k (M)

    1. Front Matter

      Pages 91-91
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    2. Introduction

      • Edward R. Fadell, Sufian Y. Husseini
      Pages 93-94

    3. The Algebra H*(\( {\Bbb F}\) k (M);ℤ)

      • Edward R. Fadell, Sufian Y. Husseini
      Pages 95-115

    4. Cellular Models

      • Edward R. Fadell, Sufian Y. Husseini
      Pages 117-151

    5. Cellular Chain Models

      • Edward R. Fadell, Sufian Y. Husseini
      Pages 153-163

  4. Homology and Cohomology of Loop Spaces

    1. Front Matter

      Pages 165-165
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    2. Introduction

      • Edward R. Fadell, Sufian Y. Husseini
      Pages 167-169

    3. The Algebra H *(Ω\( {\Bbb F}\) k (M)))

      • Edward R. Fadell, Sufian Y. Husseini
      Pages 171-185

    4. RPT-Constructions

      • Edward R. Fadell, Sufian Y. Husseini
      Pages 187-206

    5. Cellular Chain Algebra Models

      • Edward R. Fadell, Sufian Y. Husseini
      Pages 207-223

    6. The Serre Spectral Sequence

      • Edward R. Fadell, Sufian Y. Husseini
      Pages 225-242

    7. Computation of H *(Λ(M))

      • Edward R. Fadell, Sufian Y. Husseini
      Pages 243-267

    8. Γ-Category and Ends

      • Edward R. Fadell, Sufian Y. Husseini
      Pages 269-291
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Mathematics, University of Wisconsin-Madison, Madison, USA

    Edward R. Fadell, Sufian Y. Husseini

Bibliographic Information

  • Book Title: Geometry and Topology of Configuration Spaces

  • Authors: Edward R. Fadell, Sufian Y. Husseini

  • Series Title: Springer Monographs in Mathematics

  • DOI: https://doi.org/10.1007/978-3-642-56446-8

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2001

  • Hardcover ISBN: 978-3-540-66669-1Published: 27 November 2000

  • Softcover ISBN: 978-3-642-63077-4Published: 09 October 2012

  • eBook ISBN: 978-3-642-56446-8Published: 06 December 2012

  • Series ISSN: 1439-7382

  • Series E-ISSN: 2196-9922

  • Edition Number: 1

  • Number of Pages: XVI, 313

  • Topics: Geometry, Algebraic Topology, Global Analysis and Analysis on Manifolds

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