Convexity of strata in diagonal pants graphs of surfaces
Shackleton, K. J.
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Aramayona, J. Lecuire, C.; Parlier, H.; Shackleton, K. J. (2013). Convexity of strata in diagonal pants graphs of surfaces. Publicacions Matemàtiques 57 (1), 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.