Thurston’s asymmetric metrics for Anosov representations

León Carvajales; Xian Dai; Beatrice Pozzetti; Anna Wienhard

doi:10.4171/ggd/810

JournalsggdVol. 19, No. 3pp. 731–796

Thurston’s asymmetric metrics for Anosov representations

León Carvajales
Universidad de la República, Montevideo, Uruguay
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Xian Dai
Ruhr-Universität Bochum, Germany
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Beatrice Pozzetti
Ruprecht-Karls Universität 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. 19 (2025), no. 3, pp. 731–796

DOI 10.4171/GGD/810