Convexity of strata in diagonal pants graphs of surfaces

Cyril Lecuire; Hugo Parlier; Javier Aramayona; Kenneth J. Shackleton

arxiv: 1111.1187 · v1 · pith:2AWAEFKRnew · submitted 2011-11-04 · 🧮 math.GT

Convexity of strata in diagonal pants graphs of surfaces

Javier Aramayona , Cyril Lecuire , Hugo Parlier , Kenneth J. Shackleton This is my paper

classification 🧮 math.GT

keywords diagonalpantsstrataconvexitygraphanalogycompletionconsequence

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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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Convexity of strata in diagonal pants graphs of surfaces

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