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SUMMARY:Using strong contraction to obtain hyperbolicity [MPIM]
DTSTART:20251030T140000Z
DTEND:20251030T150000Z
DTSTAMP:20260415T104900Z
UID:indico-event-868@math-events.uni-bonn.de
DESCRIPTION:Speakers: Stefanie Zbinden (Universität Bonn)\n\nOberseminar 
 Differentialgeometrie\nIf a group contains a strongly contracting element\
 , then it is acylindrically hyperbolic. Moreover\, one can use the Project
 ion Complex of Bestvina\, Bromberg and Fujiwara to construct an action on 
 a hyperbolic space where said element acts loxodromically. However\, the a
 ction depends on the chosen element and other strongly contracting element
 s are not necessarily loxodromic. It raises the questions whether there ex
 ists a single action on a hyperbolic space where all strongly contracting 
 elements act loxodromically. In this talk\, we answer the above question p
 ositively by introducing the contraction space construction. In work with 
 Davide Spriano and Cornelia Drutu\, we use the contraction space to extend
  the following dichotomy known for CAT(0) groups to other groups such as i
 njective groups. Either the group has linear divergence\, in which case al
 l asymptotic cones are cut-point free\, or the group has a Morse geodesic\
 , in which case all asymptotic cones have cut-points and the group is acyl
 indrically hyperbolic.\n\nhttps://math-events.uni-bonn.de/event/868/
LOCATION:MPIM\, Vivatsgasse\,  7 - Lecture Hall (Max Planck Institute for 
 Mathematics)
URL:https://math-events.uni-bonn.de/event/868/
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