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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.
Author: Santiago Lopez de Medrano
Publisher: Springer Science & Business Media
ISBN: 3642650120
Category : Mathematics
Languages : en
Pages : 114
Get Book
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.
Author: Santiago López de Medrano
Publisher:
ISBN: 9780387050928
Category : Manifolds (Mathematics)
Languages : en
Pages : 102
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Book Description
Author: Ellen Rose Stone
Publisher:
ISBN:
Category : Involutes (Mathematics)
Languages : en
Pages : 86
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Book Description
Author: Pierre E. Conner
Publisher:
ISBN:
Category : Differentiable manifolds
Languages : en
Pages : 20
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Book Description
Author: CAMERON AUTOR GORDON
Publisher: American Mathematical Soc.
ISBN: 0821850334
Category : Mathematics
Languages : en
Pages : 528
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Book Description
These are the proceedings of the Summer Research Conference on 4-manifolds held at Durham, New Hampshire, July 1982, under the auspices of the American Mathematical Society and National Science Foundation. The conference was highlighted by the breakthroughs of Michael Freedman and S. K. Donaldson and by Frank Quinn's completion at the conference of the proof of the annulus conjecture. (We commend the AMS committee, particularly Julius Shaneson, who had the foresight in Spring 1981 to choose the subject, 4-manifolds, in which such remarkable activity was imminent.) Freedman and several others spoke on his work; some of their talks are represented by papers in this volume. Donaldson and Clifford H. Taubes gave surveys of their work on gauge theory and 4-manifolds and their papers are also included herein. There were a variety of other lectures, including Quinn's surprise, and a couple of problem sessions which led to the problem list. A background of basic differential topology is adequate for potential readers.
Author: Allen Henry Back
Publisher:
ISBN:
Category :
Languages : en
Pages : 250
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Book Description
Author: Myung Mi Myung
Publisher:
ISBN:
Category : Topology
Languages : en
Pages : 94
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Book Description
Author: José María Montesinos-Amilibia
Publisher: Springer Science & Business Media
ISBN: 3642615724
Category : Mathematics
Languages : en
Pages : 248
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Book Description
This unusual book, richly illustrated with 29 colour illustrations and about 200 line drawings, explores the relationship between classical tessellations and three-manifolds. In his original and entertaining style, the author provides graduate students with a source of geometrical insight into low-dimensional topology. Researchers in this field will find here an account of a theory that is on the one hand known to them but here is "clothed in a different garb" and can be used as a source for seminars on low-dimensional topology, or for preparing independent study projects for students, or again as the basis of a reading course.
Author: Reinhard Schultz
Publisher: American Mathematical Soc.
ISBN: 0821850385
Category : Mathematics
Languages : en
Pages : 568
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Book Description
Not merely an account of new results, this book is also a guide to motivation behind present work and potential future developments. Readers can obtain an overall understanding of the sorts of problems one studies in group actions and the methods used to study such problems. The book will be accessible to advanced graduate students who have had the equivalent of three semesters of graduate courses in topology; some previous acquaintance with the fundamentals of transformation groups is also highly desirable. The articles in this book are mainly based upon lectures at the 1983 AMS-IMS-SIAM Joint Summer Research Conference, Group Actions on Manifolds, held at the University of Colorado. A major objective was to provide an overall account of current knowledge in transformation groups; a number of survey articles describe the present state of the subject from several complementary perspectives. The book also contains some research articles, generally dealing with results presented at the conference. Finally, there is a discussion of current problems on group actions and an acknowledgment of the work and influence of D. Montgomery on the subject.
Author: Donald Keith Showers
Publisher:
ISBN:
Category : Manifolds (Mathematics)
Languages : en
Pages : 66
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Book Description
