Quasi-isometry and commensurability classification of certain right-angled Coxeter groups
Groups acting on CAT(0) spaces September 27, 2016 - September 30, 2016
Location: MSRI: Simons Auditorium
non-positive curvature
CAT(0) space
Symmetric space
buildings and complexes
group actions
57-XX - Manifolds and cell complexes {For complex manifolds, see 32Qxx}
58D05 - Groups of diffeomorphisms and homeomorphisms as manifolds [See also 22E65, 57S05]
20F55 - Reflection and Coxeter groups [See also 22E40, 51F15]
20F34 - Fundamental groups and their automorphisms [See also 57M05, 57Sxx]
20F29 - Representations of groups as automorphism groups of algebraic systems
20F65 - Geometric group theory [See also 05C25, 20E08, 57Mxx]
14622
Bowditch's JSJ tree is a quasi-isometry invariant for one-ended hyperbolic groups, which uses the local cut point structure of their visual boundary. We compute this tree for a large family of hyperbolic right-angled Coxeter groups, and identify a subfamily for which this tree is a complete quasi-isometry invariant. We then investigate the commensurability classification of groups in this subfamily. For our work on commensurability, a key step is proving that these Coxeter groups are virtually geometric amalgams of surfaces. This is joint work with Pallavi Dani (Louisiana State University) and Emily Stark (University of Haifa).
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14622
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