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SUMMARY:Hyperbolic and relatively hyperbolic groups with 2-sphere boundary
  - Genevieve  Walsh (Tufts University)
DTSTART:20250715T104500Z
DTEND:20250715T114500Z
UID:TALK233560@talks.cam.ac.uk
DESCRIPTION:We define a "drilling" of a hyperbolic group along a maximal i
 nfinite cyclic subgroup\, which results in a relatively hyperbolic group p
 air.&nbsp\; This procedure is inspired by drilling a hyperbolic 3-manifold
  along an embedded geodesic.&nbsp\; We show that\, under suitable circumst
 ances\, drilling a hyperbolic group with 2-sphere hyperbolic boundary resu
 lts in a relatively hyperbolic group with 2-sphere relatively hyperbolic b
 oundary.&nbsp\; This is joint work with D. Groves\, P. Haissinsky\, D. Osa
 jda\, and A. Sisto. If time permits\, I will discuss a somewhat related re
 sult with E. Stark which implies that a hyperbolic space which admits a ge
 ometric action and admits a relatively hyperbolic action with rank -2 abel
 ian peripheral subgroups is quasi-isometric to $H^3$.&nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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