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 defined by automata, connectivity properties and Σ-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 Šunić; 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 Σ-invariants of Thompson's group F via Morse Theory Stefan Witzel and Matthew C. B. Zaremsky.
N. Broaddus is Associate Professor of Mathematics at Ohio State University. M. Davis is Professor of Mathematics at Ohio State University. He is the author of The Geometry and Topology of Coxeter Groups (2007). J.-F. Lafont is Professor of Mathematics at Ohio State University. He is an author of Rigidity of High Dimensional Graph Manifolds (2015). His research focuses on the geometry, topology, and dynamics of spaces of non-positive curvature. I. J. Ortiz is Professor of Mathematics at Miami University. Her research focuses on K-theory of infinite groups with torsion.
