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SUMMARY:Virtual homological torsion and profinite rigidity of words - Jona
 than Fruchter (University of Bonn)
DTSTART:20250731T104500Z
DTEND:20250731T114500Z
UID:TALK234295@talks.cam.ac.uk
DESCRIPTION:A word w in a free group F is profinitely rigid if any other w
 ord that "behaves the same" as w in all finite quotients of F is related t
 o w by an automorphism of F. Conjecturally\, all words in a free group sho
 uld be profinitely rigid\, but currently only a handful of words are known
  to be profinitely rigid.\nIn this talk\, we will construct maps from bran
 ched surfaces into hyperbolic graphs of free groups with cyclic edge group
 s and use them to control torsion in the abelianization of finite-index su
 bgroups. This yields new examples of profinitely rigid words\, which preci
 sely bridge the gaps between the four previously known examples. (Based on
  joint work with Dario Ascari.)
LOCATION:Seminar Room 1\, Newton Institute
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