Tuesday, October 30Yvonne Lai, UC Davis
Through highly non-constructive methods, works by Bestvina, Culler, Morgan, Paulin, Rips, Shalen, and Thurston show that if a finitely presented group does not split over a small subgroup, then the space of its discrete and faithful actions on Hn, modulo conjugation, is compact for all dimensions. We make this result effective for Coxeter groups. By fixing a presentation and associating a simplicial tree to a given action, we find that either the group splits over a small subgroup or there is a constant C and a point in Hn that is moved no more than C by any generator. The constant C depends only on n and the number of generators in the presentation.Back to seminar home page.