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SUMMARY:Free-by-cyclic groups\, profinite rigidity and deficiency - Martin
  Bridson (University of Oxford)
DTSTART:20250707T091500Z
DTEND:20250707T101500Z
UID:TALK232804@talks.cam.ac.uk
DESCRIPTION:It is unknown whether free-by-cyclic groups can always be dist
 inguished from one another by their finite quotients\, i.e. whether they a
 re always profinitely rigid within the class of free-by-cyclic groups. Aft
 er surveying the context of this question\, I will describe joint work wit
 h Pawel Piwek in which we show that all free-by-cyclic groups with centre 
 are profinitely rigid in this sense. I shall also explain why groups of th
 is form resolve the old question of whether one can simultaneously minimis
 e the rank (number of generators) and deficiency of a finitely presented g
 roup. A key idea in the proofs is that instead of approaching these groups
  as mapping tori\, one should view them as the fundamental groups of a cer
 tain type of non-positively 2-complex.
LOCATION:Seminar Room 1\, Newton Institute
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