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

2008/07/10 by Frederic Palesi, Palesi, Frederic
Mathematics · #20F34 (Secondary) #22D40 #57M05 (Primary) #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:20F34 #msc:22D40 #msc:57M05

paper · pdf · doi:10.48550/arxiv.0807.1615

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

arxiv created 2009/01/27 · arxiv updated 2009/12/01

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.

Related

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• Ergodicity of Mapping Class Group Actions on Representation Varieties, II. Surfaces with Boundary
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• The first Johnson subgroups act ergodically on SU₂-character varieties