Journal of the European Mathematical Society

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Volume 21, Issue 11, 2019, pp. 3343–3414
DOI: 10.4171/JEMS/905

Published online: 2019-07-19

Anosov representations and dominated splittings

Jairo Bochi[1], Rafael Potrie[2] and Andrés Sambarino[3]

(1) Pontificia Universidad Católica de Chile, Santiago, Chile
(2) Universidad de la República, Montevideo, Uruguay
(3) Université Pierre et Marie Curie, Paris, France

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].

Keywords: Discrete subgroups of Lie groups, linear cocycles, dominated splitting, coarse geometry, hyperbolic groups

Bochi Jairo, Potrie Rafael, Sambarino Andrés: Anosov representations and dominated splittings. J. Eur. Math. Soc. 21 (2019), 3343-3414. doi: 10.4171/JEMS/905