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.

About the Authors

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.

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