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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
Classifying Spaces of Sporadic Groups
Hardcover ISBN:  978-0-8218-4474-8
Product Code:  SURV/147
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
eBook ISBN:  978-1-4704-1374-3
Product Code:  SURV/147.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Hardcover ISBN:  978-0-8218-4474-8
eBook: ISBN:  978-1-4704-1374-3
Product Code:  SURV/147.B
List Price: $254.00 $191.50
MAA Member Price: $228.60 $172.35
AMS Member Price: $203.20 $153.20
Classifying Spaces of Sporadic Groups
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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
Hardcover ISBN:  978-0-8218-4474-8
Product Code:  SURV/147
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
eBook ISBN:  978-1-4704-1374-3
Product Code:  SURV/147.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Hardcover ISBN:  978-0-8218-4474-8
eBook ISBN:  978-1-4704-1374-3
Product Code:  SURV/147.B
List Price: $254.00 $191.50
MAA Member Price: $228.60 $172.35
AMS Member Price: $203.20 $153.20
  • 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.

    Readership

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

  • Table of Contents
     
     
    • 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
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.

Readership

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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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