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Thurston’s asymmetric metrics for Anosov representations

  • León Carvajales

    Universidad de la República, Montevideo, Uruguay

  • Xian Dai

    Ruhr-Universität Bochum, Bochum, Germany

  • Beatrice Pozzetti

    Ruprecht-Karls Universität Heidelberg, Heidelberg, Germany

  • Anna Wienhard

    Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany
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Abstract

We provide a good dynamical framework allowing to generalize Thurston’s asymmetric metric and the associated Finsler norm from Teichmüller space to large classes of Anosov representations. In many cases, including the space of Hitchin representations, this gives a (possibly asymmetric) Finsler distance. In some cases, we explicitly compute the associated Finsler norm.

Cite this article

León Carvajales, Xian Dai, Beatrice Pozzetti, Anna Wienhard, Thurston’s asymmetric metrics for Anosov representations. Groups Geom. Dyn. (2024), published online first

DOI 10.4171/GGD/810