The Theory of Transformation Groups

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 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 differentiable 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.

Readership: First year graduate students in mathematics; research workers whose work touches on these themes.

Katsuo Kawakubo, Professor, Department of Mathematics, Osaka University, Japan

"'Throughout, much care is taken to illustrate concepts and results with examples and applications.' L'Enseignement Mathématique, 1992"

"'The book is a refreshing account of the basic tools and techniques of the theory of topological and differentiable transformation groups. The exposition and the arrangement of the material is carefully aimed to make the subject accessible to graduate students with a modest background in algebraic topology.' A.H. Assadi, Zentralblatt für Mathematik und ihre Grenzgebiete Mathematics Abstracts"

"The expressed 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. Undoubtedly, this aim has been achieved, and it is very likely that in years to come, the book will serve as an easy to read textbook on topological transformation groups." - Deutschen Mathematiker-Vereinigung, Bd. 96, Heft 4