All finitely generated 3-manifold groups are Grothendieck rigid

All finitely generated 3-manifold groups are Grothendieck rigid

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Hongbin Sun, Rutgers University

Zoom link:https://princeton.zoom.us/j/453512481?pwd=OHZ5TUJvK2trVVlUVmJLZkhIRHFDUT09

A finitely generated residually finite group G is said to be Grothendieck rigid if for any finitely generated proper subgroup H<G, the inclusion induced homomorphism \hat{H}\to \hat{G} on their profinite completions is not an isomorphism. There do exist finitely presented groups that are not Grothendieck rigid. We will prove that, if we restrict to the family of finitely generated 3-manifold groups, then all these groups are Grothendieck rigid. The proof relies on a precise description on non-separable subgroups of 3-manifold groups.