Profinite Recognition of Amalgamated Factors

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• Julian Wykowski, University of Cambridge
• Friday 20 October 2023, 13:45-14:45
• MR13.

If you have a question about this talk, please contact Macarena Arenas.

Can one detect amalgamated factors in the finite quotients of a group? In this talk, we will find out that the answer is “yes” for virtually free groups. I will introduce the theory of profinite groups acting on profinite trees and present a profinite subgroup accessibility result which connects graph of profinite groups decompositions to profinite group cohomology. I will then use this result, together with an algebraic result of Garrido—Jaikin-Zapirain and some Bass—Serre theoretic manipulations, to sketch the proof that amalgamated factors of finitely generated virtually free groups over finite amalgamation are always visible in the finite quotients of the ambient group.

This talk is part of the Geometric Group Theory (GGT) Seminar series.

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