Convexity of strata in diagonal pants graphs of surfaces

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.

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Bibliographische Detailangaben
Hauptverfasser: Aramayona, Javier, Lecuire, Cyril, Parlier, H, Shackleton, K. J
Format: Artikel
Sprache:eng
Schlagworte:
Forgetful map
Pants complex
Weil-Petersson metric
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Zusammenfassung: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.