Anosov representations and dominated splittings

By Jairo Bochi, Rafael Potrie, Andr'es Sambarino. Journal of the European Mathematical Society (Print), 2016

161 citations recorded by the source corpus.

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 Gueritaud-Guichard-Kassel-Wienhard and Kapovich-Leeb-Porti by different methods. We also give characterizations in terms of multicones and cone-types inspired in the work of Avila-Bochi-Yoccoz and Bochi-Gourmelon. Finally we provide a new proof of the higher rank Morse Lemma of Kapovich-Leeb-Porti.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/4db0403e004781c76f29b6e581481d4e4c7370f0

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In Algebra and Number Theory

In Discrete Mathematics and Combinatorics

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Citations in the corpus

The geometry of maximal representations of surface groups into SO0(2,n) (2017, unknown): “roximal. In particular, the limit curve ξ can be reconstructed from the attracting and repelling eigenvectors of ρ(γ) for γ ∈ Γ. More precisely, we have the following: Corollary 2.6 (see for instance [BPS16]). For every γ ∈ Γ\{id}, let γ+ and γ− denote the attracting and repelling ﬁxed points of γ i”
Conformality for a robust class of non-conformal attractors (2019, methodology): “As a corollary we can follow [5] and generalize to the non-Archimedean case the following important fact originally proved by Labourie [36] and Guichard-W.”
Anosov groups: local mixing, counting and equidistribution (2020, unknown): “Given the recent work [8] which introduces the geodesic flow for Anosov groups which is shown to be a metric Anosov flow, Sambarino’s proof is known to extend to all Anosov groups (see [10, Appendix]): Theorem 1.14.”