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Author :
Publisher : Academic Press
ISBN 13 : 0080873596
Total Pages : 477 pages
Book Rating : 4.0/5 (88 download)
Download or read book Introduction to Compact Transformation Groups written by and published by Academic Press. This book was released on 1972-09-29 with total page 477 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Compact Transformation Groups
Author : Bruce D. Evans
Publisher : American Mathematical Soc.
ISBN 13 : 0821822691
Total Pages : 74 pages
Book Rating : 4.8/5 (218 download)
Download or read book C^*-Bundles and Compact Transformation Groups written by Bruce D. Evans and published by American Mathematical Soc.. This book was released on 1982 with total page 74 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Deane Montgomery
Publisher : Courier Dover Publications
ISBN 13 : 0486831582
Total Pages : 305 pages
Book Rating : 4.4/5 (868 download)
Download or read book Topological Transformation Groups written by Deane Montgomery and published by Courier Dover Publications. This book was released on 2018-06-13 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Katsuo Kawakubo
Publisher : Oxford University Press on Demand
ISBN 13 : 9780198532125
Total Pages : 338 pages
Book Rating : 4.5/5 (321 download)
Download or read book The Theory of Transformation Groups written by Katsuo Kawakubo and published by Oxford University Press on Demand. This book was released on 1991 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Markus Stroppel
Publisher : European Mathematical Society
ISBN 13 : 9783037190166
Total Pages : 320 pages
Book Rating : 4.1/5 (91 download)
Download or read book Locally Compact Groups written by Markus Stroppel and published by European Mathematical Society. This book was released on 2006 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Locally compact groups play an important role in many areas of mathematics as well as in physics. The class of locally compact groups admits a strong structure theory, which allows to reduce many problems to groups constructed in various ways from the additive group of real numbers, the classical linear groups and from finite groups. The book gives a systematic and detailed introduction to the highlights of that theory. In the beginning, a review of fundamental tools from topology and the elementary theory of topological groups and transformation groups is presented. Completions, Haar integral, applications to linear representations culminating in the Peter-Weyl Theorem are treated. Pontryagin duality for locally compact Abelian groups forms a central topic of the book. Applications are given, including results about the structure of locally compact Abelian groups, and a structure theory for locally compact rings leading to the classification of locally compact fields. Topological semigroups are discussed in a separate chapter, with special attention to their relations to groups. The last chapter reviews results related to Hilbert's Fifth Problem, with the focus on structural results for non-Abelian connected locally compact groups that can be derived using approximation by Lie groups. The book is self-contained and is addressed to advanced undergraduate or graduate students in mathematics or physics. It can be used for one-semester courses on topological groups, on locally compact Abelian groups, or on topological algebra. Suggestions on course design are given in the preface. Each chapter is accompanied by a set of exercises that have been tested in classes.
Author : T. Tom Dieck
Publisher : Springer
ISBN 13 : 3540385177
Total Pages : 317 pages
Book Rating : 4.5/5 (43 download)
Download or read book Transformation Groups and Representation Theory written by T. Tom Dieck and published by Springer. This book was released on 2006-11-15 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Armand Borel
Publisher : Princeton University Press
ISBN 13 : 9780691090948
Total Pages : 262 pages
Book Rating : 4.0/5 (99 download)
Download or read book Seminar on Transformation Groups written by Armand Borel and published by Princeton University Press. This book was released on 1960 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: The description for this book, Seminar on Transformation Groups. (AM-46), Volume 46, will be forthcoming.
Author : I.M. James
Publisher : Springer Science & Business Media
ISBN 13 : 1461382831
Total Pages : 253 pages
Book Rating : 4.4/5 (613 download)
Download or read book General Topology and Homotopy Theory written by I.M. James and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: Students of topology rightly complain that much of the basic material in the subject cannot easily be found in the literature, at least not in a convenient form. In this book I have tried to take a fresh look at some of this basic material and to organize it in a coherent fashion. The text is as self-contained as I could reasonably make it and should be quite accessible to anyone who has an elementary knowledge of point-set topology and group theory. This book is based on a course of 16 graduate lectures given at Oxford and elsewhere from time to time. In a course of that length one cannot discuss too many topics without being unduly superficial. However, this was never intended as a treatise on the subject but rather as a short introductory course which will, I hope, prove useful to specialists and non-specialists alike. The introduction contains a description of the contents. No algebraic or differen tial topology is involved, although I have borne in mind the needs of students of those branches of the subject. Exercises for the reader are scattered throughout the text, while suggestions for further reading are contained in the lists of references at the end of each chapter. In most cases these lists include the main sources I have drawn on, but this is not the type of book where it is practicable to give a reference for everything.
Author : Shoshichi Kobayashi
Publisher : Springer Science & Business Media
ISBN 13 : 3642619819
Total Pages : 192 pages
Book Rating : 4.6/5 (426 download)
Download or read book Transformation Groups in Differential Geometry written by Shoshichi Kobayashi and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: Given a mathematical structure, one of the basic associated mathematical objects is its automorphism group. The object of this book is to give a biased account of automorphism groups of differential geometric struc tures. All geometric structures are not created equal; some are creations of ~ods while others are products of lesser human minds. Amongst the former, Riemannian and complex structures stand out for their beauty and wealth. A major portion of this book is therefore devoted to these two structures. Chapter I describes a general theory of automorphisms of geometric structures with emphasis on the question of when the automorphism group can be given a Lie group structure. Basic theorems in this regard are presented in §§ 3, 4 and 5. The concept of G-structure or that of pseudo-group structure enables us to treat most of the interesting geo metric structures in a unified manner. In § 8, we sketch the relationship between the two concepts. Chapter I is so arranged that the reader who is primarily interested in Riemannian, complex, conformal and projective structures can skip §§ 5, 6, 7 and 8. This chapter is partly based on lec tures I gave in Tokyo and Berkeley in 1965.
Author : Eldar Straume
Publisher : American Mathematical Soc.
ISBN 13 : 0821804839
Total Pages : 90 pages
Book Rating : 4.8/5 (218 download)
Download or read book Compact Connected Lie Transformation Groups on Spheres with Low Cohomogeneity. II written by Eldar Straume and published by American Mathematical Soc.. This book was released on 1997 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 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. We are concerned with the classification of differentiable compact connected Lie transformation groups on (homology) spheres, with [italic]c [less than or equal to symbol] 2, and the main results are summarized in five theorems, A, B, C, D, and E in part I. This paper is part II of the project, and addresses theorems D and E. D examines the orthogonal model from theorem A and orbit structures, while theorem E addresses the existence of "exotic" [italic capital]G-spheres.
Author : Eldar Straume
Publisher : American Mathematical Soc.
ISBN 13 : 082180409X
Total Pages : 106 pages
Book Rating : 4.8/5 (218 download)
Download or read book Compact Connected Lie Transformation Groups on Spheres with Low Cohomogeneity, I written by Eldar Straume and published by American Mathematical Soc.. This book was released on 1996 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 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.
Author : Edward G. Effros
Publisher : American Mathematical Soc.
ISBN 13 : 0821812750
Total Pages : 99 pages
Book Rating : 4.8/5 (218 download)
Download or read book Locally Compact Transformation Groups and C^*-Algebras written by Edward G. Effros and published by American Mathematical Soc.. This book was released on 1967 with total page 99 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Tammo tom Dieck
Publisher : Walter de Gruyter
ISBN 13 : 3110858371
Total Pages : 325 pages
Book Rating : 4.1/5 (18 download)
Download or read book Transformation Groups written by Tammo tom Dieck and published by Walter de Gruyter. This book was released on 2011-04-20 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: “This book is a jewel – it explains important, useful and deep topics in Algebraic Topology that you won’t find elsewhere, carefully and in detail.” Prof. Günter M. Ziegler, TU Berlin
Author : H. T Ku
Publisher : Springer
ISBN 13 : 3540380639
Total Pages : 465 pages
Book Rating : 4.5/5 (43 download)
Download or read book Proceedings of the Second Conference on Compact Transformation Groups. University of Massachusetts, Amherst, 1971 written by H. T Ku and published by Springer. This book was released on 2006-11-15 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Tammo tom Dieck
Publisher : Springer
ISBN 13 : 3540460365
Total Pages : 311 pages
Book Rating : 4.5/5 (44 download)
Download or read book Algebraic Topology and Transformation Groups written by Tammo tom Dieck and published by Springer. This book was released on 2006-11-14 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Anthony Bak
Publisher : Springer Science & Business Media
ISBN 13 : 9781402007835
Total Pages : 272 pages
Book Rating : 4.0/5 (78 download)
Download or read book Current Trends in Transformation Groups written by Anthony Bak and published by Springer Science & Business Media. This book was released on 2002-07-31 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : C. Allday
Publisher : Cambridge University Press
ISBN 13 : 0521350220
Total Pages : 486 pages
Book Rating : 4.5/5 (213 download)
Download or read book Cohomological Methods in Transformation Groups written by C. Allday and published by Cambridge University Press. This book was released on 1993-07 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
