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arXiv · 1810.07891

Excursions of generic geodesics in right-angled Artin groups and graph products

Yulan Qing·Giulio Tiozzo
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Abstract

Motivated by the notion of cusp excursion in geometrically finite hyperbolic manifolds, we define a notion of excursion in any subgroup of a given group, and study its asymptotic distribution for right-angled Artin groups and graph products. In particular, for any irreducible right-angled Artin group we show that with respect to the counting measure, the maximal excursion of a generic geodesic in any flat tends to $\log n$, where $n$ is the length of the geodesic. In this regard, irreducible RAAGs behave like a free product of groups. In fact, we show that the asymptotic distribution of excursions detects the growth rate of the RAAG and whether it is reducible.

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Yulan Qing, Giulio Tiozzo. 2018-10-18. Excursions of generic geodesics in right-angled Artin groups and graph products. https://arxiv.org/abs/1810.07891

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