BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Using strong contraction to obtain hyperbolicity - Stefanie Zbinde
 n (Rheinische Friedrich-Wilhelms-Universität Bonn)
DTSTART:20250708T081500Z
DTEND:20250708T091500Z
UID:TALK232816@talks.cam.ac.uk
DESCRIPTION:If a group contains a strongly contracting element\, then it i
 s acylindrically hyperbolic. Moreover\, one can use the Projection Complex
  of Bestvina\, Bromberg and Fujiwara to construct an action on a hyperboli
 c space where said element acts loxodromically. However\, the action depen
 ds on the chosen element and other strongly contracting elements are not n
 ecessarily loxodromic. It raises the questions whether there exists a sing
 le action on a hyperbolic space where all strongly contracting elements ac
 t loxodromically.\nIn this talk\, we answer the above question positively 
 by introducing the contraction space construction. Together with Cornelia 
 Druțu and Davide Spriano we then show that the contraction space can be u
 sed to extend the following dichotomy known for CAT(0) groups to other gro
 ups such as injective groups. Either the group has linear divergence\, in 
 which case all asymptotic cones are cut-point free\, or the group has a Mo
 rse geodesic\, in which case all asymptotic cones have cut-points and the 
 group is acylindrically hyperbolic.
LOCATION:Seminar Room 1\, Newton Institute
END:VEVENT
END:VCALENDAR