| The Theory of Transformation Groups Contributor(s): Kawakubo, Katsuo (Author) |
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ISBN: 0198532121 ISBN-13: 9780198532125 Publisher: Oxford University Press, USA OUR PRICE: $133.00 Product Type: Hardcover Published: January 1992 Annotation: 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. |
| Additional Information |
| BISAC Categories: - Mathematics | Number Theory - Mathematics | Transformations - Language Arts & Disciplines | Linguistics - General |
| Dewey: 512.72 |
| LCCN: 91002840 |
| Physical Information: 1.1" H x 6.12" W x 9.44" (1.60 lbs) 348 pages |
| Descriptions, Reviews, Etc. |
| Publisher 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. |