Convexity of strata in diagonal pants graphs of surfaces
arXiv:1111.1187
Abstract
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.
arXiv comment14 pages, 4 figures