Totally geodesic subgraphs of the pants complex

• Autores: Javier Aramayona Delgado , Hugo Parlier, Kenneth J. Shackleton
• Localización: Mathematical research letters, ISSN 1073-2780, Vol. 15, Nº 2-3, 2008, págs. 309-320
• Idioma: inglés
• DOI: 10.4310/mrl.2008.v15.n2.a9
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• Resumen

  • 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.