Fibered commensurability and arithmeticity of random mapping tori
Groups, geometry, and dynamics, Tome 11 (2017) no. 4, pp. 1253-1279
Voir la notice de l'article provenant de la source EMS Press
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 H. We further assume that H 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.
Classification :
20-XX, 57-XX, 60-XX
Mots-clés : Random walk, mapping class group, fibered commensurability, arithmetic 3-manifold
Mots-clés : Random walk, mapping class group, fibered commensurability, arithmetic 3-manifold
Affiliations des auteurs :
Hidetoshi Masai 1
Hidetoshi Masai. Fibered commensurability and arithmeticity of random mapping tori. Groups, geometry, and dynamics, Tome 11 (2017) no. 4, pp. 1253-1279. doi: 10.4171/ggd/428
@article{10_4171_ggd_428,
author = {Hidetoshi Masai},
title = {Fibered commensurability and arithmeticity of random mapping tori},
journal = {Groups, geometry, and dynamics},
pages = {1253--1279},
year = {2017},
volume = {11},
number = {4},
doi = {10.4171/ggd/428},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/428/}
}
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