Involutions on Manifolds

Involutions on Manifolds PDF Author: Santiago Lopez de Medrano
Publisher: Springer Science & Business Media
ISBN: 3642650120
Category : Mathematics
Languages : en
Pages : 114

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Book Description
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.

Involutions on Manifolds

Involutions on Manifolds PDF Author: Santiago Lopez de Medrano
Publisher: Springer Science & Business Media
ISBN: 3642650120
Category : Mathematics
Languages : en
Pages : 114

Get Book Here

Book Description
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.

Involutions on Manifolds

Involutions on Manifolds PDF Author: Ellen Rose Stone
Publisher:
ISBN:
Category : Involutes (Mathematics)
Languages : en
Pages : 86

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Involutions on Grassman Manifolds

Involutions on Grassman Manifolds PDF Author: Allen Henry Back
Publisher:
ISBN:
Category :
Languages : en
Pages : 250

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PL Involutions of Some 3-manifolds

PL Involutions of Some 3-manifolds PDF Author: Myung Mi Myung
Publisher:
ISBN:
Category : Topology
Languages : en
Pages : 94

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Differentiable Involutions

Differentiable Involutions PDF Author: Pierre E. Conner
Publisher:
ISBN:
Category : Differentiable manifolds
Languages : en
Pages : 20

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PL Involutions on Lens Spaces and Other 3-manifolds

PL Involutions on Lens Spaces and Other 3-manifolds PDF Author: Paik Kee Kim
Publisher:
ISBN:
Category : Manifolds (Mathematics)
Languages : en
Pages : 80

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Involutions of 3-manifolds with a 2-dimensional Fixed Point Set Component

Involutions of 3-manifolds with a 2-dimensional Fixed Point Set Component PDF Author: Donald Keith Showers
Publisher:
ISBN:
Category : Manifolds (Mathematics)
Languages : en
Pages : 66

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Surgery on Compact Manifolds

Surgery on Compact Manifolds PDF Author: Charles Terence Clegg Wall
Publisher: American Mathematical Soc.
ISBN: 0821809423
Category : Mathematics
Languages : en
Pages : 321

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Book Description
The publication of this book in 1970 marked the culmination of a period in the history of the topology of manifolds. This edition, based on the original text, is supplemented by notes on subsequent developments and updated references and commentaries.

Foundational Essays on Topological Manifolds, Smoothings, and Triangulations. (AM-88), Volume 88

Foundational Essays on Topological Manifolds, Smoothings, and Triangulations. (AM-88), Volume 88 PDF Author: Robion C. Kirby
Publisher: Princeton University Press
ISBN: 1400881501
Category : Mathematics
Languages : en
Pages : 368

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Book Description
Since Poincaré's time, topologists have been most concerned with three species of manifold. The most primitive of these--the TOP manifolds--remained rather mysterious until 1968, when Kirby discovered his now famous torus unfurling device. A period of rapid progress with TOP manifolds ensued, including, in 1969, Siebenmann's refutation of the Hauptvermutung and the Triangulation Conjecture. Here is the first connected account of Kirby's and Siebenmann's basic research in this area. The five sections of this book are introduced by three articles by the authors that initially appeared between 1968 and 1970. Appendices provide a full discussion of the classification of homotopy tori, including Casson's unpublished work and a consideration of periodicity in topological surgery.

Knot Theory and Manifolds

Knot Theory and Manifolds PDF Author: Dale Rolfsen
Publisher: Springer
ISBN: 3540396160
Category : Mathematics
Languages : en
Pages : 168

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