Anosov representations and dominated splittings

Abstract

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].