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Spaces of Homotopy Self-Equivalences - A Survey

  • Book
  • © 1997

Overview

Authors:
  1. John W. Rutter
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1662)

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Table of contents (22 chapters)

  1. Front Matter

    Pages I-IX
    Download chapter PDF

  2. Preliminaries

    • John W. Rutter
    Pages 1-3

  3. Building blocks

    • John W. Rutter
    Pages 4-6

  4. Representations: homology and homotopy

    • John W. Rutter
    Pages 7-10

  5. Surfaces

    • John W. Rutter
    Pages 11-18

  6. Generators: surface, modular groups

    • John W. Rutter
    Pages 19-27

  7. Manifolds of dimension three or more

    • John W. Rutter
    Pages 28-33

  8. É›*(X) not finitely generated

    • John W. Rutter
    Pages 34-35

  9. Localization

    • John W. Rutter
    Pages 36-39

  10. É›*(X) finitely presented, nilpotent

    • John W. Rutter
    Pages 40-43

  11. L-R duality

    • John W. Rutter
    Pages 44-44

  12. Cellular/homology complexes: methods

    • John W. Rutter
    Pages 45-53

  13. Cellular, homology complexes: calculations

    • John W. Rutter
    Pages 54-62

  14. Non-1-connected postnikov: methods

    • John W. Rutter
    Pages 63-73

  15. Homotopy systems, chain complexes

    • John W. Rutter
    Pages 74-79

  16. Non-1-connected spaces: calculations

    • John W. Rutter
    Pages 80-93

  17. Whitehead torsion, simple homotopy

    • John W. Rutter
    Pages 94-97

  18. Unions and products

    • John W. Rutter
    Pages 98-107

  19. Group theoretic properties

    • John W. Rutter
    Pages 108-112

  20. Homotopy type, homotopy groups

    • John W. Rutter
    Pages 113-120
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Keywords

About this book

This survey covers groups of homotopy self-equivalence classes of topological spaces, and the homotopy type of spaces of homotopy self-equivalences. For manifolds, the full group of equivalences and the mapping class group are compared, as are the corresponding spaces. Included are methods of calculation, numerous calculations, finite generation results, Whitehead torsion and other areas. Some 330 references are given. The book assumes familiarity with cell complexes, homology and homotopy. Graduate students and established researchers can use it for learning, for reference, and to determine the current state of knowledge.

Bibliographic Information

  • Book Title: Spaces of Homotopy Self-Equivalences - A Survey

  • Authors: John W. Rutter

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0093736

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1997

  • Softcover ISBN: 978-3-540-63103-3Published: 25 August 1997

  • eBook ISBN: 978-3-540-69135-8Published: 14 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: X, 170

  • Topics: Algebraic Topology

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