BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Alex Margolis (Vanderbilt University) DTSTART:20201110T160000Z DTEND:20201110T170000Z DTSTAMP:20260423T004637Z UID:OSUGGT/16 DESCRIPTION:Title: Topological completions of quasi-actions and discretisable spaces\nby Alex Margolis (Vanderbilt University) as part of Ohio State Topology and G eometric Group Theory Seminar\n\n\nAbstract\nA fundamental problem in geom etric group theory is the\nstudy of quasi-actions. We introduce and inves tigate discretisable\nspaces: spaces for which every cobounded quasi-actio n can be\nquasi-conjugated to an isometric action on a locally finite grap h. Work\nof Mosher-Sageev-Whyte shows that non-abelian free groups are\ndi scretisable\, but the property holds much more generally. For instance\,\n every non-elementary hyperbolic group that is not virtually isomorphic\nto a cocompact lattice in rank one Lie group is discretisable.\n\nAlong the way\, we study the coarse geometry of groups containing almost\nnormal/com mensurated subgroups\, and we introduce the concept of the\ntopological co mpletion of a quasi-action. The topological completion is\na locally compa ct group\, well-defined up to a compact normal subgroup\,\nreflecting the geometry of the quasi-action. We give several\napplications of the tools w e develop. For instance we show that any\nfinitely generated group quasi-i sometric to a ‬Z‭-by-hyperbolic group is\nalso Z-by-hyperbolic\, and p rove quasi-isometric rigidity for a large\nclass of right-angled Artin gro ups.\n LOCATION:https://researchseminars.org/talk/OSUGGT/16/ END:VEVENT END:VCALENDAR