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Convexity of strata in diagonal pants graphs of surfaces

Aramayona, Javier ; Lecuire, Cyril ; Parlier, Hugo ; Shackleton, Kenneth J.

In: Publicacions Matemàtiques, 2012, vol. 57, no. 1, p. 219-237

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.