Involutions on Manifolds

1. Front Matter

   Pages N1-IX

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2. Introduction

   • Santiago López de Medrano

   Pages 1-6

3. Notation, Conventions, Preliminaries

   • Santiago López de Medrano

   Pages 7-9

4. The Browder-Livesay Invariants

   • Santiago López de Medrano

   Pages 10-17

5. Realization of the Browder-Livesay Invariants

   • Santiago López de Medrano

   Pages 18-27

6. Relations with Non-simply-connected Surgery Obstructions

   • Santiago López de Medrano

   Pages 28-38

7. Combinatorial Classification of Involutions

   • Santiago López de Medrano

   Pages 39-54

8. Smooth Involutions

   • Santiago López de Medrano

   Pages 55-77

9. Codimension 2 Invariant Spheres

   • Santiago López de Medrano

   Pages 78-94

10. Back Matter

    Pages 95-106

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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.

• Invariant
• Mannigfaltigkeit
• homology
• homotopy
• manifold
• proof
• theorem
• topology

• Instituto de Matemáticas, Universidad Nacional Autónoma de México, México

  Santiago López de Medrano

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