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SUMMARY:A cubical Rips construction - Macarena Arenas\, University of Camb
 ridge
DTSTART:20220211T160000Z
DTEND:20220211T170000Z
UID:TALK168107@talks.cam.ac.uk
CONTACT:Macarena Arenas
DESCRIPTION:The Rips exact sequence is a useful tool for producing example
 s of groups satisfying combinations of properties that are not obviously c
 ompatible.  It works by taking as an input an arbitrary finitely presented
  group Q\, and producing as an output a hyperbolic group G that maps onto 
 Q with finitely generated kernel. The "output group" G is crafted by addin
 g generators and relations to a presentation of Q\, in such a way that the
 se relations create enough "noise" in the presentation to ensure hyperboli
 city. One can then lift pathological properties of Q to (some subgroup of)
  G. Among other things\, Rips used his construction to produce the first e
 xamples of incoherent hyperbolic groups\, and of hyperbolic groups with un
 solvable generalised word problem.\n \nIn this talk\, I will explain Rips
 ’ result\, mention some of its variations\, and survey some tools and co
 ncepts related to these constructions\, including small cancellation theor
 y\, cubulated groups\, and asphericity. Time permitting\, I will describe 
 a variation of the Rips construction that produces cubulated hyperbolic gr
 oups of any desired cohomological dimension.\n
LOCATION:MR13
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