Kasra Rafi (Toronto) - Strong Contractibility of geodesics in the mapping class group

Geometry of Teichmüller space and mapping class groups
9 April 2018

Abstract: We show that the axis of a pseudo-Anosov homeomorphism in the mapping class group may not have the strong contractibility property. Specifically, we show that, after choosing a generating set carefully, one can find a pseudo-Anosov homeomorphism f, a sequence of points x_k and a sequence of radii R_k so that the ball B(x_k, R_k) is disjoint from the axis of f, but the closest point projection of B(x_k, R_k) to the axis of f has a diameter at least c log(R_k). Along the way we show how, in certain situations, the distance between two points in the mapping class group can be computed precisely, not just up to a multiplicative error. This is a joint work in Yvon Verberne.