Resumen de Totally geodesic subgraphs of the pants complex

Javier Aramayona Delgado , Hugo Parlier, Kenneth J. Shackleton

• 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.