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Regular Languages for Contracting Geodesics

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arxiv 1809.02692 v3 pith:ILI5GHXX submitted 2018-09-07 math.GR math.GT

Joshua Eike , Abdul Zalloum This is my paper · ORCID
classification math.GRmath.GT
keywords contractingfinitelygeneratedgeodesicsgrouplanguageregularacylindrically
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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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  1. The local-to-global property for Morse quasi-geodesics

    math.GR 2019-08 conditional novelty 7.0 of 10

    Morse quasi-geodesics behave locally-to-globally in mapping class groups, CAT(0) groups, 3-manifold groups, and relatively hyperbolic groups, giving new combination theorems for stable subgroups.

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