Finitely generated subgroups vs. normal subgroups in 3-manifold groups

Geometry & Topology
Event time: 
Thursday, March 31, 2005 - 11:30am to Wednesday, March 30, 2005 - 7:00pm
431 DL
Yair Glasner
Speaker affiliation: 
University of Illinois at Chicago
Event description: 

This is joint work with Pete Storm and Juan Souto.
Let G be the fundamental group of a 3 dimensional hyperbolic manifold of finite volume.
We define an invariant topology on G, by taking the normal subgroups and
their cosets as a basis for the topology.
This is a refinement of the profinite topology.

We prove that every finitely generated subgroup of G is closed in this topology.
As a corollary we deduce that a maximal subgroup of infinite index in G cannot
be finitely generated.