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SUMMARY:Hyperplanes all over the place - Abdul Zalloum (Queen's University
 \, Canada)
DTSTART:20211029T124500Z
DTEND:20211029T134500Z
UID:TALK162484@talks.cam.ac.uk
CONTACT:76015
DESCRIPTION:(Joint with Petyt and Spriano) A revolutionary work of Sageev 
 shows that the entire structure of a CAT (0) cube complex is encoded in th
 e combinatorics of its hyperplanes. I will describe a very natural way in 
 which hyperplanes exist beyond the world of CAT (0) cube complexes includi
 ng CAT (0) spaces/groups\, hierarchically hyperbolic groups\, and coarse m
 edian spaces that satisfy an extra condition. Using such hyperplanes\, we 
 build a family of hyperbolic spaces in the same fashion the contact graph 
 of Hagen and the separation graph of Genevious are built. For instance\, i
 n the mapping class group case\, the "contact graph" we build coincides (u
 p to quasi-isometry) with the curve graph\, and in RAAGS\, the contact gra
 ph we build coincides with the contact graph of Hagen\, up to quasi-isomet
 ry. A great deal of the well-known theorems regarding the actions on such 
 graphs almost effortlessly carry through from the world of cubulated group
 s to our setting. The main new class of groups our work provides a ``conta
 ct graph" for is the class of CAT (0) groups.
LOCATION:Zoom https://maths-cam-ac-uk.zoom.us/j/95208706709
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