On profinite properties of free-by-cyclic groups

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• Monika Kudlinska (Oxford)
• Friday 28 April 2023, 13:45-14:45
• MR13.

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A central question in Geometric Group Theory is to determine how much algebraic information is encoded in the set of finite quotients of a given group. Much work has been done towards solving this problem for fundamental groups of 3-manifolds. In this talk, we will focus our attention on a related family of groups known as free-by-cyclic groups, which have natural connections with 3-manifolds. We will see that many properties of free-by-cyclic groups are invariants of their profinite completion. As a consequence, we obtain various profinite rigidity results, including the almost profinite rigidity of generic free-by-cyclic groups amongst the class of all free-by-cyclic groups. This is based on joint work with Sam Hughes.

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

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