JournalsggdVol. 19, No. 3pp. 731–796

Thurston’s asymmetric metrics for Anosov representations

  • León Carvajales

    Universidad de la República, Montevideo, Uruguay
    ORCID

  • Xian Dai

    Ruhr-Universität Bochum, Germany
    ORCID

  • Beatrice Pozzetti

    Ruprecht-Karls Universität Heidelberg, Germany
    ORCID

  • Anna Wienhard

    Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany
    ORCID
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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. 19 (2025), no. 3, pp. 731–796

DOI 10.4171/GGD/810