Ergodic actions of mapping class groups on moduli spaces of representations of non-orientable surfaces

Frederic Palesi

Published 2008-07-10, updated 2009-01-27Version 3

The purpose of this paper is to study the action of the mapping class group on the moduli space of representations of the fundamental group of a non-orientable surface into SU(2). The action is shown to be ergodic with respect to a natural measure. This measure is defined using the push-forward measure associated to a map defined by the presentation of the surface group. given by the pushforward of Haar measure. This result is an extension of earlier results of Goldman for orientable surfaces.