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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Veröffentlicht in:Publicacions Matemàtiques 2013, Vol.57 (1), p.219-237, Article 219
Hauptverfasser: Aramayona, J., Lecuire, C., Parlier, H., Shackleton, K. J.
Format: Artikel
Sprache:eng
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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.
ISSN:0214-1493
2014-4350
DOI:10.5565/PUBLMAT_57113_08