Distortion and Tits alternative in smooth mapping class groups
Dynamical Systems
2016-10-21 v4 Group Theory
Geometric Topology
Abstract
In this article, we study the smooth mapping class group of a surface S relative to a given Cantor set, that is the group of isotopy classes of orientation-preserving smooth diffeomorphisms of S which preserve this Cantor set. When the Cantor set is the standard ternary Cantor set, we prove that the subgroup consisting of diffeomorphisms which are isotopic to the identity on S does not contain any distorted elements. Moreover, we prove a weak Tits alternative for these groups.
Keywords
Cite
@article{arxiv.1506.02877,
title = {Distortion and Tits alternative in smooth mapping class groups},
author = {Sebastian Hurtado and Emmanuel Militon},
journal= {arXiv preprint arXiv:1506.02877},
year = {2016}
}
Comments
Theorem 1.1. has been improved in this version