Topology and Geometry Seminar

Title: Pseudo-Anosov mapping classes with small dilatation from graphs

Speaker: Eriko Hironaka

Abstract: Heuristically there are reasons to think that mapping classes with small complexity should arise from simple graphs. We describe two ways to construct pseudo-Anosov maps from graphs, and relate their dilatations to spectral radius of the adjacency matrix. The first construction is due to Thurston, and is a way to construct orientable pseudo-Anosov maps from bipartite graphs. The second construction uses labeled graphs. A particular case was used in work with E. Kin to give an explicit of a family of mapping classes with dilatations giving the best known asymptotics as a function of genus. Together these two families give the smallest known dilatations for mapping classes of low genus.