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

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

2008-07-10

arxiv.org/abs/0807.1615v3

Mathematics

Geometric Topology

41 pages, 12 figures, third version. New section added

Scientific paper

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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