Subgroup complexes / Stephen D. Smith.

Format:

Book

Author/Creator:

Smith, Stephen D., 1948- author.

Series:

Mathematical surveys and monographs ; Volume 179.

Mathematical surveys and monographs ; Volume 179

Language:

English

Subjects (All):

Finite groups.

Group theory.

Physical Description:

1 online resource (xii, 364 pages) : illustrations.

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2011]

Language Note:

English

Summary:

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.

Contents:

Cover

Title page

Contents

Preface and acknowledgments

Introduction

Part I. Background material and examples

Background: Posets, simplicial complexes, and topology

Examples: Subgroup complexes as geometries for simple groups

Part II. Fundamental techniques

Contractibility

Homotopy equivalence

Part III. Basic applications

The reduced Euler characteristic and variations on vanishing

The reduced Lefschetz module and projectivity

Group cohomology and decompositions

Part IV. Some more advanced topics

Spheres in homology and Quillen's Conjecture

Connectivity, simple connectivity, and sphericality

Local-coefficient homology and representation theory

Orbit complexes and Alperin's Conjecture

Bibliography

Index

Back Cover.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references and index.

Description based on print version record.

Description based on publisher supplied metadata and other sources.

ISBN:

1-4704-1406-6

OCLC:

898200384