Profinitely Rigid Seifert Fibered Spaces and Grothendieck’s Problem

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• Ryan Spitler (Rice University)
• Friday 13 May 2022, 13:45-14:45
• MR15.

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One natural starting point when studying a group is to investigate its finite quotients, and one might wonder how much these finite quotients can detect about the group in question. In particular, many have recently been interested in distinguishing fundamental groups of 3-manifolds using just their finite quotients. I will discuss a few infinite families of Seifert fibered spaces whose fundamental groups can be shown to be profinitely rigid; each of these groups can be distinguished from all other finitely generated, residually finite groups by their finite quotients. I will also discuss how these 3-manifold groups can be used to create interesting examples related to Grothendieck’s problem on profinite completions. This is joint work with Martin Bridson and Alan Reid.

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

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