Topological Methods in Group Theory

doi:10.1017/9781108526203

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.

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Topological Methods in Group Theory

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Contents

Frontmatter
pp i-iv

Contents
pp v-viii

Contributors
pp ix-xii

Preface
pp xiii-xvi

1 - Left Relatively Convex Subgroups
pp 1-18

2 - Groups with Context-free Co-word Problem and Embeddings into Thompson’s Group V
pp 19-37

3 - Limit Sets for Modules over Groups Acting on a CAT(0) Space
pp 38-45

4 - Ideal Structure of the C∗-algebra of R. Thompson’s group T
pp 46-66

5 - Local Similarity Groups with Context-free Co-word Problem
pp 67-91

6 - Compacta with Shapes of Finite Complexes: a Direct Approach to the Edwards–Geoghegan–Wall
pp 92-110

7 - The Horofunction Boundary of the Lamplighter Group L2 with the Diestel–Leader metric
pp 111-134

8 - Intrinsic Geometry of a Euclidean Simplex
pp 135-145

9 - Hyperbolic Dimension and Decomposition Complexity
pp 146-167

10 - Some Remarks on the Covering Groups of a Topological Group
pp 168-172

11 - The Σ-invariants of Thompson’s group F via Morse Theory
pp 173-194

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