Transformation Groups
Title | Transformation Groups PDF eBook |
Author | Tammo tom Dieck |
Publisher | Walter de Gruyter |
Pages | 325 |
Release | 2011-04-20 |
Genre | Mathematics |
ISBN | 3110858371 |
“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
Algebraic Topology and Transformation Groups
Title | Algebraic Topology and Transformation Groups PDF eBook |
Author | Tammo tom Dieck |
Publisher | Springer |
Pages | 311 |
Release | 2006-11-14 |
Genre | Mathematics |
ISBN | 3540460365 |
Transformation Groups and Algebraic K-Theory
Title | Transformation Groups and Algebraic K-Theory PDF eBook |
Author | Wolfgang Lück |
Publisher | Springer |
Pages | 455 |
Release | 2006-11-14 |
Genre | Mathematics |
ISBN | 3540468277 |
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.
Transformation Groups and Representation Theory
Title | Transformation Groups and Representation Theory PDF eBook |
Author | T. Tom Dieck |
Publisher | Springer |
Pages | 317 |
Release | 2006-11-15 |
Genre | Mathematics |
ISBN | 3540385177 |
Cohomology Theory of Topological Transformation Groups
Title | Cohomology Theory of Topological Transformation Groups PDF eBook |
Author | W.Y. Hsiang |
Publisher | Springer Science & Business Media |
Pages | 175 |
Release | 2012-12-06 |
Genre | Mathematics |
ISBN | 3642660525 |
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.
Topological Transformation Groups
Title | Topological Transformation Groups PDF eBook |
Author | Deane Montgomery |
Publisher | Courier Dover Publications |
Pages | 305 |
Release | 2018-06-13 |
Genre | Mathematics |
ISBN | 0486831582 |
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.
Seminar on Transformation Groups
Title | Seminar on Transformation Groups PDF eBook |
Author | Armand Borel |
Publisher | Princeton University Press |
Pages | 260 |
Release | 1960 |
Genre | Mathematics |
ISBN | 0691090947 |
Armond Borel’s influential seminar on transformation groups from the acclaimed Annals of Mathematics Studies series Princeton University Press is proud to have published the Annals of Mathematics Studies since 1940. One of the oldest and most respected series in science publishing, it has included many of the most important and influential mathematical works of the twentieth century. The series continues this tradition as Princeton University Press publishes the major works of the twenty-first century. To mark the continued success of the series, all books are available in paperback and as ebooks.