Lanterna Rally

Author: Katsuo Kawakubo

Publisher: Oxford University Press on Demand

Published: 1991

Total Pages: 338

ISBN-13: 9780198532125

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 undergraduatedegree 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 halfof 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.