"Introduction to topological transformation groups, accessible at the early graduate level." --The American Mathematical Monthly
"Develops almost every concept under consideration slowly and from scratch. Most claims are proved in detail. Many of the important constructions are explained with examples. Each chapter has a list of problems. The author extracts some of the fundamental concepts from these sources, adds his own ideas, and in this way produces a very readable text." --Mathematical Reviews
Product Description
This book presents 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 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 undergraduate degree 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 differential manifolds and Lie groups with particular emphasis on fibre bundles and characteristic classes. The latter half of 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.
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