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SUMMARY:A cubical Rips Construction - Macarena Arenas (University of Cambr
 idge)
DTSTART:20220311T134500Z
DTEND:20220311T144500Z
UID:TALK170627@talks.cam.ac.uk
CONTACT:76015
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 w
 ith finitely generated kernel. The “output group” G is crafted by addi
 ng generators and relations to a presentation of Q\, in such a way that th
 ese relations create enough “noise” in the presentation to ensure hype
 rbolicity. One can then lift pathological properties of Q to some subgroup
  of G. Among other things\, Rips used his construction to produce the firs
 t examples of incoherent hyperbolic groups\, and of hyperbolic groups with
  unsolvable generalised word problem.\n\n \n\nIn this talk\, I will explai
 n Rips’ result\, mention some of its variations\, and survey some tools 
 and concepts related to these constructions\, including small cancellation
  theory\, cubulated groups\, and asphericity. I will also describe a new v
 ersion of the Rips construction that produces cocompactly cubulated hyperb
 olic groups of any desired cohomological dimension.
LOCATION:In person if possible
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