AMS eBook CollectionsOne of the world's most respected mathematical collections, available in digital format for your library or institution

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/10.1090/surv/179
MathSciNet review: 2850680
MSC: Primary 20D05; Secondary 20E42, 55N91, 55U10

View full volume as PDF

Read more about this volume

Table of Contents

Download chapters as PDF

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