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Subgroup Complexes

Stephen D. Smith University of Illinois at Chicago, Chicago, IL
Available Formats:
Hardcover ISBN: 978-0-8218-0501-5
Product Code: SURV/179
List Price: $105.00 MAA Member Price:$94.50
AMS Member Price: $84.00 Electronic ISBN: 978-1-4704-1406-1 Product Code: SURV/179.E List Price:$99.00
MAA Member Price: $89.10 AMS Member Price:$79.20
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List Price: $157.50 MAA Member Price:$141.75
AMS Member Price: $126.00 Click above image for expanded view Subgroup Complexes Stephen D. Smith University of Illinois at Chicago, Chicago, IL Available Formats:  Hardcover ISBN: 978-0-8218-0501-5 Product Code: SURV/179  List Price:$105.00 MAA Member Price: $94.50 AMS Member Price:$84.00
 Electronic ISBN: 978-1-4704-1406-1 Product Code: SURV/179.E
 List Price: $99.00 MAA Member Price:$89.10 AMS Member Price: $79.20 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:$157.50 MAA Member Price: $141.75 AMS Member Price:$126.00
• Book Details

Mathematical Surveys and Monographs
Volume: 1792011; 364 pp
MSC: Primary 20; 05; 55;

This book is intended as an overview of a research area that combines geometries for groups (such as Tits buildings and generalizations), topological aspects of simplicial complexes from $p$-subgroups of a group (in the spirit of Brown, Quillen, and Webb), and combinatorics of partially ordered sets. The material is intended to serve as an advanced graduate-level text and partly as a general reference on the research area. The treatment offers optional tracks for the reader interested in buildings, geometries for sporadic simple groups, and $G$-equivariant equivalences and homology for subgroup complexes.

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

• Chapters
• Introduction
• Part 1. Background material and examples
• 1. Background: Posets, simplicial complexes, and topology
• 2. Examples: Subgroup complexes as geometries for simple groups
• Part 2. Fundamental techniques
• 3. Contractibility
• 4. Homotopy equivalence
• Basic applications
• 5. The reduced Euler characteristic ${\tilde {\chi }}$ and variations on vanishing
• 6. The reduced Lefschetz module ${\tilde {L}}$ and projectivity
• 7. Group cohomology and decompositions
• Part 3. Some more advanced topics
• 8. Spheres in homology and Quillen’s Conjecture
• 9. Connectivity, simple connectivity, and sphericality
• 10. Local-coefficient homology and representation theory
• 11. Orbit complexes and Alperin’s Conjecture

• Reviews

• There is an informal and conversational style to the description, designed to lead the reader through the story. This is extremely valuable for motivation and accessibility...

Mathematical Reviews
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Volume: 1792011; 364 pp
MSC: Primary 20; 05; 55;

This book is intended as an overview of a research area that combines geometries for groups (such as Tits buildings and generalizations), topological aspects of simplicial complexes from $p$-subgroups of a group (in the spirit of Brown, Quillen, and Webb), and combinatorics of partially ordered sets. The material is intended to serve as an advanced graduate-level text and partly as a general reference on the research area. The treatment offers optional tracks for the reader interested in buildings, geometries for sporadic simple groups, and $G$-equivariant equivalences and homology for subgroup complexes.

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

• Chapters
• Introduction
• Part 1. Background material and examples
• 1. Background: Posets, simplicial complexes, and topology
• 2. Examples: Subgroup complexes as geometries for simple groups
• Part 2. Fundamental techniques
• 3. Contractibility
• 4. Homotopy equivalence
• Basic applications
• 5. The reduced Euler characteristic ${\tilde {\chi }}$ and variations on vanishing
• 6. The reduced Lefschetz module ${\tilde {L}}$ and projectivity
• 7. Group cohomology and decompositions
• Part 3. Some more advanced topics
• 8. Spheres in homology and Quillen’s Conjecture
• 9. Connectivity, simple connectivity, and sphericality
• 10. Local-coefficient homology and representation theory
• 11. Orbit complexes and Alperin’s Conjecture
• There is an informal and conversational style to the description, designed to lead the reader through the story. This is extremely valuable for motivation and accessibility...

Mathematical Reviews
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