Anosov representations and dominated splittings

  • Jairo Bochi

    Pontificia Universidad Católica de Chile, Santiago, Chile
  • Rafael Potrie

    Universidad de la República, Montevideo, Uruguay
  • Andrés Sambarino

    Université Pierre et Marie Curie, Paris, France
Anosov representations and dominated splittings cover

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We provide a link between Anosov representations introduced by Labourie and dominated splitting of linear cocycles. This allows us to obtain equivalent characterizations for Anosov representations and to recover recent results due to Guéritaud–Guichard–Kassel–Wienhard [GGKW] and Kapovich–Leeb–Porti [KLP2] by different methods. We also give characterizations in terms of multicones and cone types inspired by the work of Avila–Bochi–Yoccoz [ABY] and Bochi–Gourmelon [BG]. Finally, we provide a new proof of the higher rank Morse Lemma of Kapovich–Leeb–Porti [KLP2].

Cite this article

Jairo Bochi, Rafael Potrie, Andrés Sambarino, Anosov representations and dominated splittings. J. Eur. Math. Soc. 21 (2019), no. 11, pp. 3343–3414

DOI 10.4171/JEMS/905