JournalsggdVol. 11, No. 4pp. 1253–1279

Fibered commensurability and arithmeticity of random mapping tori

  • Hidetoshi Masai

    Tohoku University, Japan
Fibered commensurability and arithmeticity of random mapping tori cover

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Abstract

We consider a random walk on the mapping class group of a surface of finite type. We assume that the random walk is determined by a probability measure whose support is finite and generates a non-elementary subgroup HH. We further assume that HH is not consisting only of lifts with respect to any one covering. Then we prove that the probability that such a random walk gives a non-minimal mapping class in its fibered commensurability class decays exponentially. As an application of the minimality, we prove that for the case where a surface has at least one puncture, the probability that a random walk gives mapping classes with arithmetic mapping tori decays exponentially. We also prove that a random walk gives rise to asymmetric mapping tori with exponentially high probability for closed case.

Cite this article

Hidetoshi Masai, Fibered commensurability and arithmeticity of random mapping tori. Groups Geom. Dyn. 11 (2017), no. 4, pp. 1253–1279

DOI 10.4171/GGD/428