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Virtual homological torsion and profinite rigidity of words

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OGGW01 - Discrete and profinite groups

A word w in a free group F is profinitely rigid if any other word that “behaves the same” as w in all finite quotients of F is related to w by an automorphism of F. Conjecturally, all words in a free group should be profinitely rigid, but currently only a handful of words are known to be profinitely rigid. In this talk, we will construct maps from branched surfaces into hyperbolic graphs of free groups with cyclic edge groups and use them to control torsion in the abelianization of finite-index subgroups. This yields new examples of profinitely rigid words, which precisely bridge the gaps between the four previously known examples. (Based on joint work with Dario Ascari.)

This talk is part of the Isaac Newton Institute Seminar Series series.

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