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SUMMARY:Hyperplanes all over the place  - Abdul Zalloum (Queen's Universit
 y\, Canada)
DTSTART:20220204T134500Z
DTEND:20220204T144500Z
UID:TALK167720@talks.cam.ac.uk
CONTACT:76015
DESCRIPTION:(Joint with Petyt and Spriano) A revolutionary work of Sageev\
 nshows that the entire structure of a CAT (0) cube complex is encoded in t
 he combinatorics of its hyperplanes. I will describe a very natural way in
  which hyperplanes exist beyond the world of CAT (0) cube complexes includ
 ing CAT (0) \nspaces/groups\, hierarchically hyperbolic groups\, and coars
 e median spaces that satisfy an extra condition. Using such hyperplanes\, 
 we build a family of hyperbolic spaces in the same fashion the contact gra
 ph of Hagen and the separation graph of Genevious are built. For instance\
 , in the mapping class group case\, the ?contact graph? we build coincides
  (up to quasi-isometry) with the curve graph\, and in RAAGS \, the contact
  graph we build coincides with the contact graph of Hagen\, up to quasi-is
 ometry. A great deal of the well-known theorems regarding the actions on s
 uch graphs almost effortlessly carry through from the world of cubulated g
 roups to our setting. The main new class of groups our work provides a "co
 ntact graph" for is the class of CAT (0) groups. 
LOCATION:Zoom
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