The theory of transformation groups / Katsuo Kawakubo

Traduction de: Henkan gunronAuteur principal : Kawakubo, Katsuo, 1942-1999, AuteurType de document : MonographieLangue : anglais ; de l'oeuvre originale, japonnais.Pays: Grande Bretagne.Éditeur : Oxford : Oxford University Press, 1991Description : 1 vol. (X-338 p.) : fig. ; 24 cmISBN: 0198532121.Bibliographie : Bibliogr. p. 327-333. Index.Sujet MSC : 57-02, Research exposition (monographs, survey articles) pertaining to manifolds and cell complexes
57S15, Manifolds and cell complexes - Topological transformation groups, Compact Lie groups of differentiable transformations
58J20, Global analysis, analysis on manifolds - PDEs on manifolds; differential operators, Index theory and related fixed-point theorems on manifolds
55N91, Homology and cohomology theories in algebraic topology, Equivariant homology and cohomology
57R91, Manifolds and cell complexes - Differential topology, Equivariant algebraic topology of manifoldsEn-ligne : Zentralblatt | MathSciNet
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Bibliogr. p. 327-333. Index

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. (Source : OUP)

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