Topological Methods in Group Theory

Details some of the most recent developments at the interface of topology and geometric group theory. Ideal for graduate students.

N. Broaddus (Edited by), M. Davis (Edited by), J. -F. Lafont (Edited by), I. J. Ortiz (Edited by)

9781108437622, Cambridge University Press

Paperback / softback, published 6 September 2018

208 pages, 15 b/w illus.
22.8 x 15.2 x 1.3 cm, 0.33 kg

This volume collects the proceedings of the conference 'Topological methods in group theory', held at Ohio State University in 2014 in honor of Ross Geoghegan's 70th birthday. It consists of eleven peer-reviewed papers on some of the most recent developments at the interface of topology and geometric group theory. The authors have given particular attention to clear exposition, making this volume especially useful for graduate students and for mathematicians in other areas interested in gaining a taste of this rich and active field. A wide cross-section of topics in geometric group theory and topology are represented, including left-orderable groups, groups de?ned by automata, connectivity properties and ?-invariants of groups, amenability and non-amenability problems, and boundaries of certain groups. Also included are topics that are more geometric or topological in nature, such as the geometry of simplices, decomposition complexity of certain groups, and problems in shape theory.

List of contributors
1. Left relatively convex subgroups Yago Antolín, Warren Dicks and Zoran Šuni?
2. Groups with context-free co-word problem and embeddings into Thompson's group V Rose Berns-Zieve, Dana Fry, Johnny Gillings, Hannah Hoganson and Heather Mathews
3. Limit sets for modules over groups acting on a CAT(0) space Robert Bieri and Ross Geoghegan
4. Ideal structure of the C*-algebra of R. Thompson's group T Collin Bleak and Kate Juschenko
5. Local similarity groups with context-free co-word problem Daniel Farley
6. Compacta with shapes of finite complexes: a direct approach to the Edwards–Geoghegan–Wall obstruction Craig R. Guilbault
7. The horofunction boundary of the lamplighter group L2 with the Diestel-Leader metric Keith Jones and Gregory A. Kelsey
8. Intrinsic geometry of a Euclidean simplex Barry Minemyer
9. Hyperbolic dimension and decomposition complexity Andrew Nicas and David Rosenthal
10. Some remarks on the covering groups of a topological group Dongwen Qi
11. The ?-invariants of Thompson's group F via Morse Theory Stefan Witzel and Matthew C. B. Zaremsky.

Subject Areas: Topology [PBP], Groups & group theory [PBG], Algebra [PBF]