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Regular Languages for Contracting Geodesics (1809.02692v3)
Published 7 Sep 2018 in math.GR and math.GT
Abstract: Let $G$ be a finitely generated group. We show that for any finite generating set $A$, the language consisting of all geodesics in $Cay(G,A)$ with a contracting property is a regular language. As an application, we show that any finitely generated group containing an infinite contracting geodesic must be either virtually $\mathbb{Z}$ or acylindrically hyperbolic.
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