Fibered commensurability and arithmeticity of random mapping tori
Hidetoshi Masai
Tohoku University, Japan
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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 . We further assume that 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