Transformation groups
type: Item
instance of: scholarly article
title: Transformation groups
zbMATH Open document ID: 0611.57002
author: Tammo tom Dieck
published in: De Gruyter Studies in Mathematics
publication date: 1987-01-01T00:00:00Z
review text: This book is an introduction to the theory of transformation groups from a modern viewpoint. Considerable emphasis should be placed on the word ''introduction''. The book provides the background material in equivariant topology needed to read research papers, but is definitely not an exposition of recent research. The particular choice of topics covered is clearly related to the author's research interests, emphasizing equivariant homotopy and homology theory, Mackey functors, and the Burnside ring. There is even a brief introduction to topological representation theory. These are important tools of wide applicability and one certainly expects them to have growing significance. As would be anticipated, the quality of exposition is excellent. Tom Dieck writes very well in English, even if, as he indicates, his preference would have been German. There are many examples and exercises. The book seems quite appropriate for a graduate student familiar with nonequivariant algebraic topology who wants to learn the equivariant situation. There is minimal treatment of the topic of group actions on manifolds, which is a major area of interest in transformation groups, so this would not replace \textit{G. E. Bredon}'s ''Introduction to compact transformation groups'' (1972; Zbl 0246.57017). Rather it would add some additional topics of more recent vintage.
Mathematics Subject Classification ID: 57-02
Mathematics Subject Classification ID: 57S10
zbMATH DE Number: 3988265
zbMATH Keywords: equivariant homology
zbMATH Keywords: equivariant homotopy
zbMATH Keywords: Mackey functors
zbMATH Keywords: Burnside ring
zbMATH Keywords: topological representation theory
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3988265