Topological Methods in Group Theory

N. Broaddus, M. Davis, J. -F. Lafont, I. J. Ortiz

• Publisher: Cambridge University Press
• Year: 2018
• Print ISBN: 9781108437622
• eBook ISBN: 9781108534765
• Topic: Mathematics
• Subtopic: Topology
• Index: Mathematics

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 ?-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.

Table of contents

• Cover
• Series information
• Title page
• Copyright information
• Table of contents
• List of contributors
• Preface
• 1 Left Relatively Convex Subgroups
• 2 Groups with Context-free Co-word Problem and Embeddings into Thompson's Group V
• 3 Limit Sets for Modules over Groups Acting on a CAT(0) Space
• 4 Ideal Structure of the C*-algebra of R. Thompson's group T
• 5 Local Similarity Groups with Context-free Co-word Problem
• 6 Compacta with Shapes of Finite Complexes: a Direct Approach to the Edwards–Geoghegan–Wall Obstruction
• 7 The Horofunction Boundary of the Lamplighter Group L[sub(2)] with the Diestel–Leader metric
• 8 Intrinsic Geometry of a Euclidean Simplex
• 9 Hyperbolic Dimension and Decomposition Complexity
• 10 Some Remarks on the Covering Groups of a Topological Group
• 11 The Σ-invariants of Thompson's group F via Morse Theory