Convexity of strata in diagonal pants graphs of surfaces

Mathematics – Geometric Topology

Scientific paper

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14 pages, 4 figures

Scientific paper

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.

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