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SUMMARY:Real cubings - Mark Hagen (University of Bristol)
DTSTART:20220520T124500Z
DTEND:20220520T134500Z
UID:TALK173036@talks.cam.ac.uk
CONTACT:76015
DESCRIPTION:Median spaces generalise R-trees and CAT(0) cube complexes\, a
 nd arise in nature as asymptotic cones of many different groups.  One way 
 to build median spaces from simple ones is to start with a (possibly infin
 ite) product of trees\, and delete "quarterspaces".  I will explain what t
 his means\, and why this shows that any CAT(0) cube complex arises from th
 e version of this construction where all of the trees are [0\,1].  By repl
 acing [0\,1] with arbitrary R-trees\, and allowing slightly more complicat
 ed rules specifying which quarterspaces one can delete\, one obtains a cla
 ss of median spaces called "R-cubings"\, which generalise cube complexes a
 nd R-trees but have more structure than general median spaces.  The utilit
 y of R-cubings is the following theorem: asymptotic cones of a hierarchica
 lly hyperbolic space (e.g. mapping class groups\, right-angled Artin/Coxet
 er groups\, Teichmuller space) are bilipschitz equivalent to R-cubings.  I
  will discuss an application of this to the question of when asymptotic co
 nes of a group are independent of the parameters used to define them and\,
  time permitting\, mention some work in progress about actions on R-cubing
 s.  This is all joint work with Montserrat Casals-Ruiz and Ilya Kazachkov.
LOCATION:MR11
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