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Author : A. L. Onishchik
Publisher : Unknown
Page : 324 pages
File Size : 47,6 Mb
Release : 1994
Category : Mathematics
ISBN : UOM:39015032284187
Author : A. L. Onishchik
Publisher : Unknown
Page : 315 pages
File Size : 44,9 Mb
Release : 1994-01
Category : Electronic
ISBN : 3527402624
Author : Deane Montgomery,Leo Zippin
Publisher : Courier Dover Publications
Page : 304 pages
File Size : 41,5 Mb
Release : 2018-06-13
Category : Mathematics
ISBN : 9780486831589
An advanced monograph on the subject of topological transformation groups, this volume summarizes important research conducted during a period of lively activity in this area of mathematics. The book is of particular note because it represents the culmination of research by authors Deane Montgomery and Leo Zippin, undertaken in collaboration with Andrew Gleason of Harvard University, that led to their solution of a well-known mathematical conjecture, Hilbert's Fifth Problem. The treatment begins with an examination of topological spaces and groups and proceeds to locally compact groups and groups with no small subgroups. Subsequent chapters address approximation by Lie groups and transformation groups, concluding with an exploration of compact transformation groups.
Author : Anonim
Publisher : Academic Press
Page : 458 pages
File Size : 54,8 Mb
Release : 1972-09-29
Category : Mathematics
ISBN : 0080873596
Introduction to Compact Transformation Groups
Author : T. Tom Dieck
Publisher : Springer
Page : 317 pages
File Size : 49,6 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540385172
Author : Sergeĭ Vasilʹevich Duzhin,Boris Dmitrievich Chebotarevskiĭ
Publisher : American Mathematical Soc.
Page : 246 pages
File Size : 43,6 Mb
Release : 2004
Category : Mathematics
ISBN : 9780821836439
This book is intended for undergraduate students and all those interested in mathematics. Its goal is to give an easy introduction to the concept of a transformation group using examples from different areas of mathematics. The warm-up of the first two chapters includes a discussion of algebraic operations on points in the plane, and of Euclidean plane movements. Then the notions of a transformation group and of an abstract group are introduced. Group actions, orbits, and invariants constitute the subject of the next chapter. The book concludes with an elementary exposition of the basic ideas of Sophus Lie about symmetries of differential equations. The book contains plenty of figures, as well as many exercises with hints and solutions, which help the reader to master the material.
Author : W.Y. Hsiang
Publisher : Springer Science & Business Media
Page : 175 pages
File Size : 40,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642660528
Historically, applications of algebraic topology to the study of topological transformation groups were originated in the work of L. E. 1. Brouwer on periodic transformations and, a little later, in the beautiful fixed point theorem ofP. A. Smith for prime periodic maps on homology spheres. Upon comparing the fixed point theorem of Smith with its predecessors, the fixed point theorems of Brouwer and Lefschetz, one finds that it is possible, at least for the case of homology spheres, to upgrade the conclusion of mere existence (or non-existence) to the actual determination of the homology type of the fixed point set, if the map is assumed to be prime periodic. The pioneer result of P. A. Smith clearly suggests a fruitful general direction of studying topological transformation groups in the framework of algebraic topology. Naturally, the immediate problems following the Smith fixed point theorem are to generalize it both in the direction of replacing the homology spheres by spaces of more general topological types and in the direction of replacing the group tl by more general compact groups.
Author : Armand Borel
Publisher : Princeton University Press
Page : 262 pages
File Size : 40,5 Mb
Release : 1960
Category : Mathematics
ISBN : 0691090947
The description for this book, Seminar on Transformation Groups. (AM-46), Volume 46, will be forthcoming.
Author : R.V. Gamkrelidze
Publisher : Routledge
Page : 544 pages
File Size : 42,6 Mb
Release : 2018-12-12
Category : Mathematics
ISBN : 9781351407939
Offering the insights of L.S. Pontryagin, one of the foremost thinkers in modern mathematics, the second volume in this four-volume set examines the nature and processes that make up topological groups. Already hailed as the leading work in this subject for its abundance of examples and its thorough explanations, the text is arranged so that readers can follow the material either sequentially or schematically. Stand-alone chapters cover such topics as topological division rings, linear representations of compact topological groups, and the concept of a lie group.
Author : Eldar Straume
Publisher : American Mathematical Soc.
Page : 93 pages
File Size : 52,9 Mb
Release : 1996
Category : Mathematics
ISBN : 9780821804094
This text is aimed at researchers studying Lie transformation groups.
Author : Edward G. Effros,Frank Hahn,Frank John Hahn
Publisher : American Mathematical Soc.
Page : 92 pages
File Size : 52,6 Mb
Release : 1967
Category : Algebras, Linear
ISBN : 9780821812754
Author : Marcos M. Alexandrino,Renato G. Bettiol
Publisher : Springer
Page : 213 pages
File Size : 53,7 Mb
Release : 2015-05-22
Category : Mathematics
ISBN : 9783319166131
This book provides quick access to the theory of Lie groups and isometric actions on smooth manifolds, using a concise geometric approach. After a gentle introduction to the subject, some of its recent applications to active research areas are explored, keeping a constant connection with the basic material. The topics discussed include polar actions, singular Riemannian foliations, cohomogeneity one actions, and positively curved manifolds with many symmetries. This book stems from the experience gathered by the authors in several lectures along the years and was designed to be as self-contained as possible. It is intended for advanced undergraduates, graduate students and young researchers in geometry and can be used for a one-semester course or independent study.
Author : Robert Ellis,Walter Helbig Gottschalk
Publisher : Unknown
Page : 50 pages
File Size : 54,6 Mb
Release : 1958
Category : Group actions (Mathematics)
ISBN : UOM:39015095254119
Author : Dimitrij Akhiezer
Publisher : Springer Science & Business Media
Page : 212 pages
File Size : 55,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783322802675
The main topic of this book is the sudy of the interaction between two major subjects of modern mathematics, namely, the theory of Lie groups with its specific methods and ways of thinking on the one hand and complex analysis with all its analytic, algebraic and geometric aspects. More specifically, the author concentrates on the double role of Lie groups in complex analysis, namely, as groups of biholomorphic self-made of certain complex analytic objects on the one hand and as a special class of complex manifolds with an additional strong structure on the other hand. The book starts from the basics of this subject and introduces the reader into many fields of recent research.
Author : P. S. Mostert
Publisher : Springer Science & Business Media
Page : 470 pages
File Size : 41,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642461415
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.
