| 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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Book DetailsMathematical Surveys and MonographsVolume: 179; 2011; 364 ppMSC: 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.
ReadershipGraduate students and research mathematicians interested in group theory and algebraic topology.
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Table of Contents
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Chapters
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Introduction
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Part 1. Background material and examples
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1. Background: Posets, simplicial complexes, and topology
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2. Examples: Subgroup complexes as geometries for simple groups
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Part 2. Fundamental techniques
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3. Contractibility
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4. Homotopy equivalence
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Basic applications
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5. The reduced Euler characteristic ${\tilde {\chi }}$ and variations on vanishing
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6. The reduced Lefschetz module ${\tilde {L}}$ and projectivity
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7. Group cohomology and decompositions
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Part 3. Some more advanced topics
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8. Spheres in homology and Quillen’s Conjecture
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9. Connectivity, simple connectivity, and sphericality
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10. Local-coefficient homology and representation theory
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11. Orbit complexes and Alperin’s Conjecture
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Additional Material
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Reviews
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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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- Book Details
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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
