The first Johnson subgroups act ergodically on SU_2-character varieties

TL;DR

This paper proves that the first Johnson subgroup of the mapping class group acts ergodically on the SU_2-character variety of a surface, using local analysis and trace function expansions.

Contribution

It establishes ergodicity of the first Johnson subgroup on SU_2-character varieties, providing a new understanding of the subgroup's dynamical properties.

Findings

First Johnson subgroup acts ergodically on SU_2-character varieties

Local description of the representation space around trivial representation

Use of Taylor expansion of trace functions in the proof

Abstract

We show that the first Johnson subgroup of the mapping class group of a surface S of genus greater than one acts ergodically on the moduli space of representations of the fundamental group of S in SU_2. Our proof relies on a local description of the latter space around the trivial representation and on the Taylor expansion of trace functions.