Dilatation vs self-intersection number for point-pushing pseudo-Anosovs

Geometry Topology Seminar
Monday, November 15, 2010 - 5:00pm for 1 hour (actually 50 minutes)
Room 326, Boyd Graduate Studies (UGA)
Spencer Dowdall – University of Chicago – sdowdall@math.uchicago.eduhttp://www.math.uchicago.edu/~sdowdall/
Dan Margalit
This talk is about the dilatations of pseudo-Anosov mapping classes obtained by pushing a marked point around a filling curve. After reviewing this "point-pushing" construction, I will give both upper and lower bounds on the dilatation in terms of the self-intersection number of the filling curve. I'll also give bounds on the least dilatation of any pseudo-Anosov in the point-pushing subgroup and describe the asymptotic dependence on self-intersection number. All of the upper bounds involve analyzing explicit examples using train tracks, and the lower bound is obtained by lifting to the universal cover and studying the images of simple closed curves.