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Involutions on Manifolds

  • Santiago López de Medrano

Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE2, volume 59)

Table of contents

  1. Front Matter
    Pages N1-IX
  2. Santiago López de Medrano
    Pages 1-6
  3. Santiago López de Medrano
    Pages 7-9
  4. Santiago López de Medrano
    Pages 10-17
  5. Santiago López de Medrano
    Pages 18-27
  6. Santiago López de Medrano
    Pages 28-38
  7. Santiago López de Medrano
    Pages 39-54
  8. Santiago López de Medrano
    Pages 55-77
  9. Santiago López de Medrano
    Pages 78-94
  10. Back Matter
    Pages 95-106

About this book

Introduction

This book contains the results of work done during the years 1967-1970 on fixed-point-free involutions on manifolds, and is an enlarged version of the author's doctoral dissertation [54J written under the direction of Professor William Browder. The subject of fixed-paint-free involutions, as part of the subject of group actions on manifolds, has been an important source of problems, examples and ideas in topology for the last four decades, and receives renewed attention every time a new technical development suggests new questions and methods ([62, 8, 24, 63J). Here we consider mainly those properties of fixed-point-free involutions that can be best studied using the techniques of surgery on manifolds. This approach to the subject was initiated by Browder and Livesay. Special attention is given here to involutions of homotopy spheres, but even for this particular case, a more general theory is very useful. Two important related topics that we do not touch here are those of involutions with fixed points, and the relationship between fixed-point-free involutions and free Sl-actions. For these topics, the reader is referred to [23J, and to [33J, [61J, [82J, respectively. The two main problems we attack are those of classification of involutions, and the existence and uniqueness of invariant submanifolds with certain properties. As will be seen, these problems are closely related. If (T, l'n) is a fixed-point-free involution of a homotopy sphere l'n, the quotient l'n/Tis called a homotopy projective space.

Keywords

Invariant Mannigfaltigkeit homology homotopy manifold proof theorem topology

Authors and affiliations

  • Santiago López de Medrano
    • 1
  1. 1.Instituto de MatemáticasUniversidad Nacional Autónoma de MéxicoMéxico

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-65012-3
  • Copyright Information Springer-Verlag Berlin Heidelberg 1971
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-65014-7
  • Online ISBN 978-3-642-65012-3
  • Series Print ISSN 0071-1136
  • Buy this book on publisher's site