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Topology/Geometry Seminar

Profinite Completions of 3-manifold groups and Hyperbolic Triangle Groups

Ryan Spitler (McMaster University)

Location:  zoom link
Date & time: Tuesday, 27 October 2020 at 3:50PM - 4:50PM

Abstract: The profinite completion of a group encodes the information of all the group's finite quotients.  For the fundamental group of a manifold, this is related to the collection of all the manifold's finite covers.  A recent object of study has been to investigate to what extent a manifold, for example a 3-manifold, is determined by the profinite completion of its fundamental group. I will discuss the relationship between the profinite completion and the representation theory of a group, and how this relates to recent work establishing that the fundamental groups of certain 3-manifolds and certain hyperbolic triangle groups are determined up to isomorphism by their profinite completions. This represents joint works with Martin Bridson, Ben McReynolds, and Alan Reid.

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