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

Frederic Palesi

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arXiv · 0807.1615

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

Frederic Palesi

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Abstract

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.

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BibTeX RIS

Frederic Palesi. 2009-01-27. Ergodic actions of mapping class groups on moduli spaces of representations of non-orientable surfaces. https://arxiv.org/abs/0807.1615

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