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Topology/Geometry Seminar

A characterization of separable subgroups of 3-manifold groups

Hongbin Sun (Rutgers)

Location:  Hill 525
Date & time: Tuesday, 04 December 2018 at 3:30AM - 4:30PM

Abstract:  The subgroup separability is a property in group theory that is closely related to low dimensional topology, especially lifting pi_1-injective immersed objects in a space to be embedded in some finite cover and the virtual Haken conjecture of 3-manifolds resolved by Agol. We give a complete characterization on which finitely generated subgroups of finitely generated 3-manifold groups are separable. Our characterization generalizes Liu's spirality character on pi_1-injective immersed surface subgroups of closed 3-manifold groups. A consequence of our characterization is that, for any compact, orientable, irreducible and boundary-irreducible 3-manifold M with nontrivial torus decomposition, pi_1(M) is LERF if and only if for any two adjacent pieces in the torus decomposition of M, at least one of them has a boundary component with genus at least 2.

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