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arXiv · 2002.07015

Eigenvalue gaps for hyperbolic groups and semigroups

Fanny Kassel·Rafael Potrie
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Abstract

Given a locally constant linear cocycle over a subshift of finite type, we show that the existence of a uniform gap between the i-th and (i+1)-th Lyapunov exponents for all invariant measures implies the existence of a dominated splitting of index i. We establish a similar result for sofic subshifts coming from word hyperbolic groups, in relation with Anosov representations of such groups. We discuss the case of finitely generated semigroups, and propose a notion of Anosov representation in this setting.

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Fanny Kassel, Rafael Potrie. 2020-02-17. Eigenvalue gaps for hyperbolic groups and semigroups. https://arxiv.org/abs/2002.07015

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