Topology of Transitive Transformation Groups
Author: A. L. Onishchik
Publisher:
Published: 1994
Total Pages: 324
ISBN-13:
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Cohomology Theory of Topological Transformation Groups
Author: W.Y. Hsiang
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 175
ISBN-13: 3642660525
DOWNLOAD EBOOKHistorically, 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.
Topological Groups
Author: R. V. Gamkrelidze
Publisher: CRC Press
Published: 1987-03-06
Total Pages: 204
ISBN-13: 9782881241338
DOWNLOAD EBOOKOffering 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.
Topological Transformation Groups
Author: Deane Montgomery
Publisher: Courier Dover Publications
Published: 2018-06-13
Total Pages: 305
ISBN-13: 0486824497
DOWNLOAD EBOOKOriginally published: New York: Interscience Publishers, Inc., 1955. An unabridged republication of: Huntington, New York: Robert E. Krieger Publishing Company, 1974.
Introduction to Compact Transformation Groups
Author:
Publisher: Academic Press
Published: 1972-09-29
Total Pages: 477
ISBN-13: 0080873596
DOWNLOAD EBOOKIntroduction to Compact Transformation Groups
Compact Connected Lie Transformation Groups on Spheres with Low Cohomogeneity, I
Author: Eldar Straume
Publisher: American Mathematical Soc.
Published: 1996
Total Pages: 106
ISBN-13: 082180409X
DOWNLOAD EBOOKThe cohomogeneity of a transformation group ([italic capitals]G, X) is, by definition, the dimension of its orbit space, [italic]c = dim [italic capitals]X, G. By enlarging this simple numerical invariant, but suitably restricted, one gradually increases the complexity of orbit structures of transformation groups. This is a natural program for classical space forms, which traditionally constitute the first canonical family of testing spaces, due to their unique combination of topological simplicity and abundance in varieties of compact differentiable transformation groups.
Lie Groups: Structure, Actions, and Representations
Author: Alan Huckleberry
Publisher: Springer Science & Business Media
Published: 2013-08-04
Total Pages: 422
ISBN-13: 1461471931
DOWNLOAD EBOOKLie Groups: Structures, Actions, and Representations, In Honor of Joseph A. Wolf on the Occasion of his 75th Birthday consists of invited expository and research articles on new developments arising from Wolf's profound contributions to mathematics. Due to Professor Wolf’s broad interests, outstanding mathematicians and scholars in a wide spectrum of mathematical fields contributed to the volume. Algebraic, geometric, and analytic methods are employed. More precisely, finite groups and classical finite dimensional, as well as infinite-dimensional Lie groups, and algebras play a role. Actions on classical symmetric spaces, and on abstract homogeneous and representation spaces are discussed. Contributions in the area of representation theory involve numerous viewpoints, including that of algebraic groups and various analytic aspects of harmonic analysis. Contributors D. Akhiezer T. Oshima A. Andrada I. Pacharoni M. L. Barberis F. Ricci L. Barchini S. Rosenberg I. Dotti N. Shimeno M. Eastwood J. Tirao V. Fischer S. Treneer T. Kobayashi C.T.C. Wall A. Korányi D. Wallace B. Kostant K. Wiboonton P. Kostelec F. Xu K.-H. Neeb O. Yakimova G. Olafsson R. Zierau B. Ørsted
Lie Groups and Geometric Aspects of Isometric Actions
Author: Marcos M. Alexandrino
Publisher: Springer
Published: 2015-05-22
Total Pages: 215
ISBN-13: 3319166131
DOWNLOAD EBOOKThis 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.
Lie Group Actions in Complex Analysis
Author: Dimitrij Akhiezer
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 212
ISBN-13: 3322802671
DOWNLOAD EBOOKThe 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.
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
DOWNLOAD EBOOKThese 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.
