Geometric and Cohomological Methods in Group Theory

by Edited by Martin R. Bridson , Peter H. Kropholler , Ian J. Leary

• ISBN13: 9780521757249
• ISBN10: 052175724X
• Edition: 1st
• Format: Paperback
• Copyright: 2009-12-07
• Publisher: Cambridge University Press

Summary

Geometric group theory is a vibrant subject at the heart of modern mathematics. It is currently enjoying a period of rapid growth and great influence marked by a deepening of its fertile interactions with logic, analysis and large-scale geometry, and striking progress has been made on classical problems at the heart of cohomological group theory. This volume provides the reader with a tour through a selection of the most important trends in the field, including limit groups, quasi-isometric rigidity, non-positive curvature in group theory, and L2-methods in geometry, topology and group theory. Major survey articles exploring recent developments in the field are supported by shorter research papers, which are written in a style that readers approaching the field for the first time will find inviting.

Table of Contents

Preface

List of participants

Notes on Sela's work: limit groups and Makanin-Razborov diagrams

Solutions to Bestvina &

Feighn's exercises on limit groups

L2-Invariants from the algebraic point of view

Constructing non-positively curved spaces and groups

Homology and dynamics in quasi-isometric rigidity of once-punctured mapping class groups

Hattori-Stallings trace and Euler characteristics for groups

Groups of small homological dimension and the Atiyah conjecture P. H. Kropholler, P. Linnell and W. LÃ1/4ck

Logarithms and assembly maps on Kn(Zl[G])

On complete resolutions

Structure theory for branch groups

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