Texas A&M
University, Department of
Mathematics, 216 Milner Hall, 21st of October 2009, 4:00-4:50
Groups and Dynamics Seminar
Free subgroups of lattices
Lewis Bowen of Texas
A&M
University
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.