Convexity of strata in diagonal pants graphs of surfaces

Javier Aramayona (1) , Cyril Lecuire (1) , Hugo Parlier (2) , Kenneth J. Shackleton

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 Department of Mathematics

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.

Domaines: Topologie géométrique [math.GT]

Javier Aramayona, Cyril Lecuire, Hugo Parlier, Kenneth J. Shackleton. Convexity of strata in diagonal pants graphs of surfaces. Publicacions Matemàtiques, 2013, 57 (1), pp.219-237. ⟨10.5565/PUBLMAT_57113_08⟩. ⟨hal-00952721⟩