Curve complex translation lengths

Geometry Topology Seminar
Monday, March 26, 2012 - 2:05pm for 1 hour (actually 50 minutes)
Skiles 005
Vaibhav Gadre – Harvard University
Dan Margalit
The curve complex C(S) of a closed orientable surface S of genusg is an infinite graph with vertices isotopy classes of essential simpleclosed curves on S with two vertices adjacent by an edge if the curves canbe isotoped to be disjoint. By a celebrated theorem of Masur-Minsky, thecurve complex is Gromov hyperbolic. Moreover, a pseudo-Anosov map f of Sacts on C(S) as a hyperbolic isometry with "north-south" dynamics and aninvariant quasi-axis. One can define an asymptotic translation length for fon C(S). In joint work with Chia-yen Tsai, we prove bounds on the minimalpseudo-Anosov asymptotic translation lengths on C(S) . We shall alsooutline related interesting results and questions.