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Classifying Spaces of Sporadic Groups
David J. Benson, University of Aberdeen, Scotland, United Kingdom, and Stephen D. Smith, University of Illinois at Chicago, IL

Mathematical Surveys and Monographs
2008; 289 pp; hardcover
Volume: 147
ISBN-10: 0-8218-4474-1
ISBN-13: 978-0-8218-4474-8
List Price: US$93
Member Price: US$74.40
Order Code: SURV/147
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See also:

Seifert Fiberings - Kyung Bai Lee and Frank Raymond

For each of the 26 sporadic finite simple groups, the authors construct a 2-completed classifying space using a homotopy decomposition in terms of classifying spaces of suitable 2-local subgroups. This construction leads to an additive decomposition of the mod 2 group cohomology. The authors also summarize the current status of knowledge in the literature about the ring structure of the mod 2 cohomology of sporadic simple groups.

This book begins with a fairly extensive initial exposition, intended for non-experts, of background material on the relevant constructions from algebraic topology, and on local geometries from group theory. The subsequent chapters then use those structures to develop the main results on individual sporadic groups.


Graduate students and research mathematicians interested in group theory and algebraic topology.


"...remarkably accessible at explaining sporadic groups and also is successful at working with the cohomology of the other simple groups."

-- SciTech Book News

"The core of the book consists of a detailed discussion of each sporadic group in turn. Very usefully however, the first half of the book consists of a tailor-made introduction to the relevant areas of algebraic topology and group theory. This coherent, modern account of the wide range of topics involved by two eminent researchers and expositors means that the book should be valuable to many more people working on the boundary between algebraic topology and group theory."

-- Mathematical Reviews

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