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SUMMARY:Homological filling functions and the word problem - Robert Kropho
 ller (Warwick)
DTSTART:20220518T150000Z
DTEND:20220518T160000Z
UID:TALK173855@talks.cam.ac.uk
CONTACT:Henry Wilton
DESCRIPTION:For finitely generated groups the word problem asks for the ex
 istence of an algorithm that takes in words in a finite generating set and
  decides if a word is trivial or not. For finitely presented groups this i
 s equivalent to the Dehn function being sub-recursive. There is an analogu
 e of the Dehn function for groups of type $FP_2$\, this function measures 
 the difficulty of filling loops in a certain space with surfaces. In joint
  work with Noel Brady and Ignat Soroko\, we give computations of the homol
 ogical filling functions for Ian Leary’s groups $G_L(S)$. We use this to
  show that there are uncountably many groups with homological filling func
 tion $n^4$. This gives groups that have sub-recursive homological filling 
 function but unsolvable word problem.
LOCATION:MR13
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