UIUC Dept. of Mathematics Seminar Calendar

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Thursday, November 5, 2009

Group Theory Seminar
1:00 pm in Altgeld Hall 347, Thursday, November 5, 2009

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Submitted by kapovitc.

Lewis Bowen (Texas A&M)
Free subgroups of lattices
Abstract: Let G be any locally compact, unimodular, metrizable group. The main result of the talk, roughly stated, is that if $F < G$ is any finitely generated free group and $\Gamma < G$ any lattice, then up to a small perturbation and passing to a finite index subgroup, F is a subgroup of $\Gamma$. This result has recently been used by Lackenby, Long and Reid to show that, for cocompact Kleinian groups, LERF implies the Lubotzky-Sarnak conjecture. Another application, due to Lackenby, is that every Kleinian group that contains a finite noncyclic subgroup is either finite, virtually free, or contains a surface subgroup.