Involutions on Manifolds - Ergebnisse Der Mathematik Und Ihrer Grenzgebiete. 2. Folge - Santiago Lopez De Medrano - Books - Springer-Verlag Berlin and Heidelberg Gm - 9783642650147 - December 7, 2011
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Santiago Lopez De Medrano
Involutions on Manifolds - Ergebnisse Der Mathematik Und Ihrer Grenzgebiete. 2. Folge Softcover Reprint of the Original 1st Ed. 1971 edition

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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.

106 pages, biography

Media Books     Paperback Book   (Book with soft cover and glued back)
Released December 7, 2011
ISBN13 9783642650147
Publishers Springer-Verlag Berlin and Heidelberg Gm
Pages 106
Dimensions 156 × 234 × 6 mm   ·   185 g
Language English  

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