Fibered commensurability and arithmeticity of random mapping tori

Hidetoshi Masai

Research output: Contribution to journalArticle

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 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 theminimality,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.

Original languageEnglish
Pages (from-to)1253-1279
Number of pages27
JournalGroups, Geometry, and Dynamics
Volume11
Issue number4
DOIs
Publication statusPublished - 2017 Jan 1

Keywords

  • Arithmetic 3-manifold
  • Fibered commensurability
  • Mapping class group
  • Random walk

ASJC Scopus subject areas

  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

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