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.
Reihe
Sprache
Zielgruppe
Illustrationen
31 b/w illus. 25 exercises
ISBN-13
978-1-139-10709-9 (9781139107099)
Schweitzer Klassifikation
Herausgeber*in
University of Oxford
Martin R. Bridson is the Whitehead Professor of Pure Mathematics at the University of Oxford. In 2006 he was awarded the Royal Society's Wolfson Research Merit Award.
University of Glasgow
Peter H. Kropholler is Professor of Pure Mathematics at the University of Glasgow.
Ohio State University
Ian J. Leary is Professor in the Department of Mathematics at Ohio State University.
Preface; List of participants; 1. Notes on Sela's work: limit groups and Makanin-Razborov diagrams M. Bestvina and M. Feighn; 2. Solutions to Bestvina & Feighn's exercises on limit groups H. Wilton; 3. L2-Invariants from the algebraic point of view W. Lück; 4. Constructing non-positively curved spaces and groups J. McCammond; 5. Homology and dynamics in quasi-isometric rigidity of once-punctured mapping class groups L. Mosher; 6. Hattori-Stallings trace and Euler characteristics for groups I. Chatterji and G. Mislin; 7. Groups of small homological dimension and the Atiyah conjecture P. H. Kropholler, P. Linnell and W. Lück; 8. Logarithms and assembly maps on Kn(Zl[G]) V. P. Snaith; 9. On complete resolutions O. Talelli; 10. Structure theory for branch groups J. S. Wilson.
