The Theory of Fusion Systems
An Algebraic Approach

The first book to deal comprehensively with the theory of fusion systems.

David A. Craven (Author)

9781107005969, Cambridge University Press

Hardback, published 23 June 2011

384 pages, 95 exercises
23.5 x 15.8 x 2.3 cm, 0.66 kg

"This very welcome book originates from a workshop on fusion systems held at the University of Birmingham in 2007 and is one of the first two texts on the subject, appearing at approximately the same time... The book serves as an excellent introduction to the subject and a guide to up to the cutting edget of current research."
Charles W. Eaton, Mathematical Reviews

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.

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.

Subject Areas: Topology [PBP], Algebra [PBF]