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David J. Benson University of Aberdeen, Aberdeen, Scotland, United Kingdom
Stephen D. Smith University of Illinois at Chicago, Chicago, IL
Available Formats:
Hardcover ISBN: 978-0-8218-4474-8
Product Code: SURV/147
List Price: $99.00 MAA Member Price:$89.10
AMS Member Price: $79.20 Electronic ISBN: 978-1-4704-1374-3 Product Code: SURV/147.E List Price:$93.00
MAA Member Price: $83.70 AMS Member Price:$74.40
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List Price: $148.50 MAA Member Price:$133.65
AMS Member Price: $118.80 Click above image for expanded view Classifying Spaces of Sporadic Groups David J. Benson University of Aberdeen, Aberdeen, Scotland, United Kingdom Stephen D. Smith University of Illinois at Chicago, Chicago, IL Available Formats:  Hardcover ISBN: 978-0-8218-4474-8 Product Code: SURV/147  List Price:$99.00 MAA Member Price: $89.10 AMS Member Price:$79.20
 Electronic ISBN: 978-1-4704-1374-3 Product Code: SURV/147.E
 List Price: $93.00 MAA Member Price:$83.70 AMS Member Price: $74.40 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$148.50 MAA Member Price: $133.65 AMS Member Price:$118.80
• Book Details

Mathematical Surveys and Monographs
Volume: 1472008; 289 pp
MSC: Primary 20; 55;

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.

• Part 1. Exposition of background material
• 1. Overview of our main results
• 2. Review of selected aspects of group cohomology
• 3. Simplicial sets and their equivalence with topological spaces
• 4. Bousfield-Kan completions and homotopy colimits
• 5. Decompositions and ample collections of $p$-subgroups
• 6. 2-local geometries for simple groups
• Part 2. Main results on sporadic groups
• 7. Decompositions for the individual sporadic groups
• 8. Details of proofs for individual groups

• Reviews

• ...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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Volume: 1472008; 289 pp
MSC: Primary 20; 55;

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.

• Part 1. Exposition of background material
• 1. Overview of our main results
• 2. Review of selected aspects of group cohomology
• 3. Simplicial sets and their equivalence with topological spaces
• 4. Bousfield-Kan completions and homotopy colimits
• 5. Decompositions and ample collections of $p$-subgroups
• 6. 2-local geometries for simple groups
• Part 2. Main results on sporadic groups
• 7. Decompositions for the individual sporadic groups
• 8. Details of proofs for individual groups
• ...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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