Convexity of strata in diagonal pants graphs of surfaces

2011/11/04 by Aramayona, Javier, Lecuire, Cyril, Parlier, Hugo +1
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1111.1187

Abstract

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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