Le vendredi 25 mai 2007 à 14:30 - salle 431Brian Bowditch
This talk is mainly about the surface subgroups. The geometry of surface subgroups of the mapping class group is essentially equivalent to the geometry of surface-by-surface groups. There are many open questions, for example it is not known if a surface-by-surface group can be hyperbolic, or indeed if it can be ``atoroidal'' in the sense of not containing any free abelian subgroup of rank 2. However one can show that, for fixed genera, there are only finitely many isomorphism classes of atoroidal surface-by-surface groups. The proof uses the geometry of the curve graph of Harvey and ideas of Masur and Minsky et al. from the proof of the ending lamination conjecture.