Topology Of Transformation Groups

Author : Deane Montgomery,Leo Zippin
Publisher : Courier Dover Publications
Page : 304 pages
File Size : 46,9 Mb
Release : 2018-06-13
Category : Mathematics
ISBN : 9780486831589

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Topological Transformation Groups by Deane Montgomery,Leo Zippin Pdf

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 : W.Y. Hsiang
Publisher : Springer Science & Business Media
Page : 175 pages
File Size : 43,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642660528

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Cohomology Theory of Topological Transformation Groups by W.Y. Hsiang Pdf

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 : Tammo tom Dieck
Publisher : Walter de Gruyter
Page : 325 pages
File Size : 54,9 Mb
Release : 2011-04-20
Category : Mathematics
ISBN : 9783110858372

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Transformation Groups by Tammo tom Dieck Pdf

“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 : A. L. Onishchik
Publisher : Unknown
Page : 315 pages
File Size : 43,6 Mb
Release : 1994-01
Category : Electronic
ISBN : 3527402624

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Topology of Transformation Groups by A. L. Onishchik Pdf

Author : A. L. Onishchik
Publisher : Unknown
Page : 324 pages
File Size : 47,6 Mb
Release : 1994
Category : Mathematics
ISBN : UOM:39015032284187

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Topology of Transitive Transformation Groups by A. L. Onishchik Pdf

Author : T. Tom Dieck
Publisher : Springer
Page : 317 pages
File Size : 45,6 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540385172

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Transformation Groups and Representation Theory by T. Tom Dieck Pdf

Author : Anonim
Publisher : Academic Press
Page : 458 pages
File Size : 46,9 Mb
Release : 1972-09-29
Category : Mathematics
ISBN : 0080873596

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Introduction to Compact Transformation Groups by Anonim Pdf

Introduction to Compact Transformation Groups

Author : Wolfgang Lück
Publisher : Springer
Page : 455 pages
File Size : 48,7 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540468271

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Transformation Groups and Algebraic K-Theory by Wolfgang Lück Pdf

The book focuses on the relation between transformation groups and algebraic K-theory. The general pattern is to assign to a geometric problem an invariant in an algebraic K-group which determines the problem. The algebraic K-theory of modules over a category is studied extensively and appplied to the fundamental category of G-space. Basic details of the theory of transformation groups sometimes hard to find in the literature, are collected here (Chapter I) for the benefit of graduate students. Chapters II and III contain advanced new material of interest to researchers working in transformation groups, algebraic K-theory or related fields.

Author : Alexander Arhangel’skii,Mikhail Tkachenko
Publisher : Springer Science & Business Media
Page : 794 pages
File Size : 49,6 Mb
Release : 2008-05-01
Category : Mathematics
ISBN : 9789491216350

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Topological Groups and Related Structures, An Introduction to Topological Algebra. by Alexander Arhangel’skii,Mikhail Tkachenko Pdf

Algebraandtopology,thetwofundamentaldomainsofmathematics,playcomplem- tary roles. Topology studies continuity and convergence and provides a general framework to study the concept of a limit. Much of topology is devoted to handling in?nite sets and in?nity itself; the methods developed are qualitative and, in a certain sense, irrational. - gebra studies all kinds of operations and provides a basis for algorithms and calculations. Very often, the methods here are ?nitistic in nature. Because of this difference in nature, algebra and topology have a strong tendency to develop independently, not in direct contact with each other. However, in applications, in higher level domains of mathematics, such as functional analysis, dynamical systems, representation theory, and others, topology and algebra come in contact most naturally. Many of the most important objects of mathematics represent a blend of algebraic and of topologicalstructures. Topologicalfunctionspacesandlineartopologicalspacesingeneral, topological groups and topological ?elds, transformation groups, topological lattices are objects of this kind. Very often an algebraic structure and a topology come naturally together; this is the case when they are both determined by the nature of the elements of the set considered (a group of transformations is a typical example). The rules that describe the relationship between a topology and an algebraic operation are almost always transparentandnatural—theoperationhastobecontinuous,jointlyorseparately.

Author : Armand Borel
Publisher : Princeton University Press
Page : 262 pages
File Size : 44,9 Mb
Release : 1960
Category : Mathematics
ISBN : 0691090947

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Seminar on Transformation Groups by Armand Borel Pdf

The description for this book, Seminar on Transformation Groups. (AM-46), Volume 46, will be forthcoming.

Author : C. Allday,V. Puppe
Publisher : Cambridge University Press
Page : 486 pages
File Size : 48,7 Mb
Release : 1993-07
Category : Mathematics
ISBN : 9780521350228

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Cohomological Methods in Transformation Groups by C. Allday,V. Puppe Pdf

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.

Author : Deane Montgomery,Leo Zippin
Publisher : Courier Dover Publications
Page : 305 pages
File Size : 53,6 Mb
Release : 2018-06-13
Category : Mathematics
ISBN : 9780486824499

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Topological Transformation Groups by Deane Montgomery,Leo Zippin Pdf

Originally published: New York: Interscience Publishers, Inc., 1955. An unabridged republication of: Huntington, New York: Robert E. Krieger Publishing Company, 1974.

Author : Sophus Lie
Publisher : Springer
Page : 640 pages
File Size : 40,7 Mb
Release : 2015-03-12
Category : Mathematics
ISBN : 9783662462119

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Theory of Transformation Groups I by Sophus Lie Pdf

This modern translation of Sophus Lie's and Friedrich Engel's “Theorie der Transformationsgruppen I” will allow readers to discover the striking conceptual clarity and remarkably systematic organizational thought of the original German text. Volume I presents a comprehensive introduction to the theory and is mainly directed towards the generalization of ideas drawn from the study of examples. The major part of the present volume offers an extremely clear translation of the lucid original. The first four chapters provide not only a translation, but also a contemporary approach, which will help present day readers to familiarize themselves with the concepts at the heart of the subject. The editor's main objective was to encourage a renewed interest in the detailed classification of Lie algebras in dimensions 1, 2 and 3, and to offer access to Sophus Lie's monumental Galois theory of continuous transformation groups, established at the end of the 19th Century. Lie groups are widespread in mathematics, playing a role in representation theory, algebraic geometry, Galois theory, the theory of partial differential equations and also in physics, for example in general relativity. This volume is of interest to researchers in Lie theory and exterior differential systems and also to historians of mathematics. The prerequisites are a basic knowledge of differential calculus, ordinary differential equations and differential geometry.

Author : Christian Rosendal
Publisher : Cambridge University Press
Page : 309 pages
File Size : 41,7 Mb
Release : 2021-12-16
Category : Mathematics
ISBN : 9781108842471

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Coarse Geometry of Topological Groups by Christian Rosendal Pdf

Provides a general framework for doing geometric group theory for non-locally-compact topological groups arising in mathematical practice.

Author : Mahender Singh,Yongjin Song,Jie Wu
Publisher : Springer
Page : 313 pages
File Size : 43,7 Mb
Release : 2019-02-02
Category : Mathematics
ISBN : 9789811357428

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Algebraic Topology and Related Topics by Mahender Singh,Yongjin Song,Jie Wu Pdf

This book highlights the latest advances in algebraic topology, from homotopy theory, braid groups, configuration spaces and toric topology, to transformation groups and the adjoining area of knot theory. It consists of well-written original research papers and survey articles by subject experts, most of which were presented at the “7th East Asian Conference on Algebraic Topology” held at the Indian Institute of Science Education and Research (IISER), Mohali, Punjab, India, from December 1 to 6, 2017. Algebraic topology is a broad area of mathematics that has seen enormous developments over the past decade, and as such this book is a valuable resource for graduate students and researchers working in the field.