Geodesic axes in the pants complex of the five-holed sphere

AbstractWe study the synthetic geometry of the pants graph of the 5-holed sphere, establishing the existence of geodesics connecting any vertex or ideal point to any ideal point. We prove the existence of geodesic axes for sufficiently high powers of any pseudo-Anosov mapping class, and that large link hierarchies from Harveyʼs curve graph all induce geodesic paths

Uniformly exponential growth and mapping class groups of surfaces

We show that the mapping class group of an orientable finite type surface has uniformly exponential growth, as well as various closely related groups. This provides further evidence that mapping class groups may be linear.Comment: 6 pages, no figure

Convexity of strata in diagonal pants graphs of surfaces

We prove a number of convexity results for strata of the diagonal pants graph of a surface, in analogy with the extrinsic geometric properties of strata in the Weil-Petersson completion. As a consequence, we exhibit convex flat subgraphs of every possible rank inside the diagonal pants graph.Comment: 14 pages, 4 figure