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arXiv · 1708.02223

Negligibility of parabolic elements in relatively hyperbolic groups

Motiejus Valiunas
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Abstract

We study density of parabolic elements in a finitely generated relatively hyperbolic group $G$ with respect to a word metric. We prove this density to be zero (apart from degenerate cases) and the limit defining the density to converge exponentially fast; this has recently been proven independently by W. Yang. As a corollary, we obtain the analogous result for the set of commuting pairs of elements in $G^2$, showing that the degree of commutativity of $G$ is equal to zero.

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Motiejus Valiunas. 2017-08-07. Negligibility of parabolic elements in relatively hyperbolic groups. https://arxiv.org/abs/1708.02223

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