Subgroup complexes

About this Title

Stephen D. Smith, University of Illinois at Chicago, Chicago, IL

Publication: Mathematical Surveys and Monographs
Publication Year: 2011; Volume 179
ISBNs: 978-0-8218-0501-5 (print); 978-1-4704-1406-1 (online)
DOI: https://doi.org/http://dx.doi.org/10.1090/surv/179
MathSciNet review: 2850680
MSC: Primary 20D05; Secondary 20E42, 55N91, 55U10

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Table of Contents

Front/Back Matter

• View this volume's front and back matter

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

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