Cohomological Methods in Transformation Groups
Cohomological Methods in Transformation Groups

Author: C. Allday

Publisher: Cambridge University Press

Published: 1993-07

Total Pages: 486

ISBN-13: 0521350220

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This is an account of the theory of certain types of compact transformation groups, namely those that are susceptible to study using ordinary cohomology theory and rational homotopy theory, which in practice means the torus groups and elementary abelian p-groups. The efforts of many mathematicians have combined to bring a depth of understanding to this area. However to make it reasonably accessible to a wide audience, the authors have streamlined the presentation, referring the reader to the literature for purely technical results and working in a simplified setting where possible. In this way the reader with a relatively modest background in algebraic topology and homology theory can penetrate rather deeply into the subject, whilst the book at the same time makes a useful reference for the more specialised reader.

Transformation Groups
Transformation Groups

Author: Goutam Mukherjee

Publisher:

Published: 2005

Total Pages: 130

ISBN-13: 9788185931548

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"The importance of cohomology theory in the study of symplectic and Hamiltonian torus actions has been recognized for a long time. The usefulness of cohomolgy theory in the field continues today, significantly in the theory of toric varieties. One of the major aims of this book is to illustrate the cohomological methods used in the study of symplectic and Hamiltonian torus actions and to present some recent results." "The other aspect of this book is to present the theory of toric manifolds, which is a study of toric varieties from a topological view point and to illustrate some applications to combinatorics. Most of the techniques used and proofs of results included, are either new and have not appeared elsewhere or are written in a style which may be more accessible to readers. The volume is suitable for graduate students in mathematics having some basic knowledge in algebraic and differential topology."--BOOK JACKET.

Proceedings of the Conference on Transformation Groups
Proceedings of the Conference on Transformation Groups

Author: P. S. Mostert

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 470

ISBN-13: 3642461417

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These Proceedings contain articles based on the lectures and in formal discussions at the Conference on Transformation Groups held at Tulane University, May 8 to June 2, 1967 under the sponsorship of the Advanced Science Seminar Projects of the National Science Foun dation (Contract No. GZ 400). They differ, however, from many such Conference proceedings in that particular emphasis has been given to the review and exposition of the state of the theory in its various mani festations, and the suggestion of direction to further research, rather than purely on the publication of research papers. That is not to say that there is no new material contained herein. On the contrary, there is an abundance of new material, many new ideas, new questions, and new conjectures~arefully incorporated within the framework of the theory as the various authors see it. An original objective of the Conference and of this report was to supply a much needed review of and supplement to the theory since the publication of the three standard works, MONTGOMERY and ZIPPIN, Topological Transformation Groups, Interscience Pub lishers, 1955, BOREL et aI. , Seminar on Transformation Groups, Annals of Math. Surveys, 1960, and CONNER and FLOYD, Differen tial Periodic Maps, Springer-Verlag, 1964. Considering this objective ambitious enough, it was decided to limit the survey to that part of Transformation Group Theory derived from the Montgomery School.

Current Trends in Transformation Groups
Current Trends in Transformation Groups

Author: Anthony Bak

Publisher: Springer Science & Business Media

Published: 2002-07-31

Total Pages: 272

ISBN-13: 9781402007835

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This book provides an overview of some of the most active topics in the theory of transformation groups over the past decades and stresses advances obtained in the last dozen years. The emphasis is on actions of Lie groups on manifolds and CW complexes. Manifolds and actions of Lie groups on them are studied in the linear, semialgebraic, definable, analytic, smooth, and topological categories. Equivalent vector bundles play an important role. The work is divided into fifteen articles and will be of interest to anyone researching or studying transformations groups. The references make it easy to find details and original accounts of the topics surveyed, including tools and theories used in these accounts.

Cohomology of Finite Groups
Cohomology of Finite Groups

Author: Alejandro Adem

Publisher: Springer Science & Business Media

Published: 2013-03-14

Total Pages: 329

ISBN-13: 3662062801

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Some Historical Background This book deals with the cohomology of groups, particularly finite ones. Historically, the subject has been one of significant interaction between algebra and topology and has directly led to the creation of such important areas of mathematics as homo logical algebra and algebraic K-theory. It arose primarily in the 1920's and 1930's independently in number theory and topology. In topology the main focus was on the work ofH. Hopf, but B. Eckmann, S. Eilenberg, and S. MacLane (among others) made significant contributions. The main thrust of the early work here was to try to understand the meanings of the low dimensional homology groups of a space X. For example, if the universal cover of X was three connected, it was known that H2(X; A. ) depends only on the fundamental group of X. Group cohomology initially appeared to explain this dependence. In number theory, group cohomology arose as a natural device for describing the main theorems of class field theory and, in particular, for describing and analyzing the Brauer group of a field. It also arose naturally in the study of group extensions, N

The Theory of Transformation Groups
The Theory of Transformation Groups

Author: Katsuo Kawakubo

Publisher: Oxford University Press on Demand

Published: 1991

Total Pages: 338

ISBN-13: 9780198532125

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The aim of this book is to present an introduction to the theory of transformation groups which will be suitable for all those coming to the subject for the first time. The emphasis is on the study of topological groups and, in particular, the study of compact Lie groups acting on manifolds.Throughout, much care is taken to illustrate concepts and results with examples and applications. Numerous exercises are also included to further extend a reader's understanding and knowledge. Prerequisites are a familiarity with algebra and topology as might have been acquired from an undergraduatedegree in Mathematics. The author begins by introducing the basic concepts of the subject such as fixed point sets, orbits, and induced transformation groups. Attention then turns to the study of differentiable manifolds and Lie groups with particular emphasis on fibre bundles and characteristic classes. The latter halfof the book is devoted to surveying the main themes of the subject: structure and decomposition theorems, the existence and uniqueness theorems of principal orbits, transfer theorems, and the Lefschetz fixed point theorem.

Transformation Groups
Transformation Groups

Author: Goutam Mukherjee

Publisher: Springer

Published: 2005-04-15

Total Pages: 140

ISBN-13: 9386279304

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Contributed lectures presented earlier at Winter School on Transformation Groups.

Algebraic Topology. Poznan 1989
Algebraic Topology. Poznan 1989

Author: Stefan Jackowski

Publisher: Springer

Published: 2006-11-14

Total Pages: 404

ISBN-13: 354047403X

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As part of the scientific activity in connection with the 70th birthday of the Adam Mickiewicz University in Poznan, an international conference on algebraic topology was held. In the resulting proceedings volume, the emphasis is on substantial survey papers, some presented at the conference, some written subsequently.