Fusion systems are a recent development in finite group theory and sit at the intersection of algebra and topology. This book is the first to deal comprehensively with this new and expanding field, taking the reader from the basics of the theory right to the state of the art. Three motivational chapters, indicating the interaction of fusion and fusion systems in group theory, representation theory and topology are followed by six chapters that explore the theory of fusion systems themselves. Starting with the basic definitions, the topics covered include: weakly normal and normal subsystems; morphisms and quotients; saturation theorems; results about control of fusion; and the local theory of fusion systems. At the end there is also a discussion of exotic fusion systems. Designed for use as a text and reference work, this book is suitable for graduate students and experts alike.
- The first book to bring together all of the literature in the field, making it accessible to first-time learners
- Almost 100 exercises aid the reader's learning
- Includes new proofs, providing multiple ways of viewing theorems
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Product details
- Date Published: June 2011
- format: Hardback
- isbn: 9781107005969
- length: 384 pages
- dimensions: 235 x 158 x 23 mm
- weight: 0.66kg
- contains: 95 exercises
- availability: Available
Table of Contents
Preface
Part I. Motivation:
1. Fusion in finite groups
2. Fusion in representation theory
3. Fusion in topology
Part II. The Theory:
4. Fusion systems
5. Weakly normal subsystems, quotients, and morphisms
6. Proving saturation
7. Control in fusion systems
8. Local theory of fusion systems
9. Exotic fusion systems
References
Index of notation
Index.
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Author
David A. Craven, University of Oxford
David A. Craven is a Junior Research Fellow in the Mathematical Institute at the University of Oxford.