Author
Bindng
Involutions on Manifolds (Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge)
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This book contains the results of work done during the years 19671970 on fixedpointfree involutions on manifolds, and is an enlarged version of the authors doctoral dissertation [54J written under the direction of Professor William Browder. The subject of fixedpaintfree 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 fixedpointfree 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 fixedpointfree involutions and free Slactions. 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, ln) is a fixedpointfree involution of a homotopy sphere ln, the quotient ln/Tis called a homotopy projective space.
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