Mathematical Research Letters

Volume 15, Issue 2, March 2008 pp. 309-320.

Totally geodesic subgraphs of the pants complex

Authors: Javier Aramayona (1), Hugo Parlier (2) , and Kenneth J. Shackleton (3)
Author institution: University of Warwick (1), Ecole Polytechnique Fédérale de Lausanne (2), and T. I. Tech. (3)

Summary: In recent work of Brock's, the pants graph is shown to be a combinatorial model for the completion of the Weil-Petersson metric on Teichm\"uller space. We prove that every Farey graph embedded in the pants graph is totally geodesic, in analogy with the extrinsic geometry of any $2$-dimensional stratum inside the Weil-Petersson completion.

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