Hardcover ISBN:  9780821844748 
Product Code:  SURV/147 
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eBook ISBN:  9781470413743 
Product Code:  SURV/147.E 
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Hardcover ISBN:  9780821844748 
eBook: ISBN:  9781470413743 
Product Code:  SURV/147.B 
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AMS Member Price:  $203.20 $153.20 
Hardcover ISBN:  9780821844748 
Product Code:  SURV/147 
List Price:  $129.00 
MAA Member Price:  $116.10 
AMS Member Price:  $103.20 
eBook ISBN:  9781470413743 
Product Code:  SURV/147.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Hardcover ISBN:  9780821844748 
eBook ISBN:  9781470413743 
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 DetailsMathematical Surveys and MonographsVolume: 147; 2008; 289 ppMSC: Primary 20; 55
For each of the 26 sporadic finite simple groups, the authors construct a 2completed classifying space using a homotopy decomposition in terms of classifying spaces of suitable 2local 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 nonexperts, 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.
ReadershipGraduate 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. BousfieldKan completions and homotopy colimits

5. Decompositions and ample collections of $p$subgroups

6. 2local 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


Additional Material

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 tailormade 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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For each of the 26 sporadic finite simple groups, the authors construct a 2completed classifying space using a homotopy decomposition in terms of classifying spaces of suitable 2local 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 nonexperts, 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. BousfieldKan completions and homotopy colimits

5. Decompositions and ample collections of $p$subgroups

6. 2local 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 tailormade 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