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CATEGORIES:Geometric Group Theory (GGT) Seminar
SUMMARY:Topological completions of quasi-actions and discr
etisable spaces - Alex Margolis (Vanderbilt Univer
sity)
DTSTART;TZID=Europe/London:20201106T134500
DTEND;TZID=Europe/London:20201106T144500
UID:TALK152827AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/152827
DESCRIPTION:A fundamental problem in geometric group theory is
the \nstudy of quasi-actions. We introduce and i
nvestigate discretisable spaces: spaces for which
every cobounded quasi-action can be quasi-conjugat
ed to an isometric action on a locally finite grap
h. Work of Mosher-Sageev-Whyte shows that free gro
ups are discretisable spaces\, but the property ho
lds much more generally. For instance\, every non-
elementary hyperbolic group is either virtually is
omorphic to a cocompact lattice in rank one Lie gr
oup\, or it is discretisable.\n\nAlong the way\, w
e introduce the concept of the topological complet
ion of a quasi-action. This is a locally compact g
roup\, well-defined up to a compact normal subgrou
p\, reflecting the geometry of the quasi-action. W
e give several applications of the tools we develo
p. For instance we show that any finitely generate
d group quasi-isometric to a Z-by-hyperbolic gro
up is also Z-by-hyperbolic\, and prove quasi-isome
tric rigidity for a large class of right-angled Ar
tin groups.\n
LOCATION:Zoom: https://maths-cam-ac-uk.zoom.us/j/9163658322
2
CONTACT:
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