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SUMMARY:Topological completions of quasi-actions and discretisable spaces 
 - Alex Margolis (Vanderbilt University)
DTSTART:20201106T134500Z
DTEND:20201106T144500Z
UID:TALK152827@talks.cam.ac.uk
CONTACT:76015
DESCRIPTION:A fundamental problem in geometric group theory is the \nstudy
  of quasi-actions.  We introduce and investigate discretisable spaces: spa
 ces for which every cobounded quasi-action can be quasi-conjugated to an i
 sometric action on a locally finite graph. Work of Mosher-Sageev-Whyte sho
 ws that free groups are discretisable spaces\, but the property holds much
  more generally. For instance\, every non-elementary hyperbolic group is e
 ither virtually isomorphic to a cocompact lattice in rank one Lie group\, 
 or it is discretisable.\n\nAlong the way\, we introduce the concept of the
  topological completion of a quasi-action. This is a locally compact group
 \, well-defined up to a compact normal subgroup\, reflecting the geometry 
 of the quasi-action. We give several applications of the tools we develop.
  For instance we show that any finitely generated group quasi-isometric to
  a ‬Z‭-by-hyperbolic group is also Z-by-hyperbolic\, and prove quasi-i
 sometric rigidity for a large class of right-angled Artin groups.\n
LOCATION:Zoom: https://maths-cam-ac-uk.zoom.us/j/91636583222
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