The first Johnson subgroups act ergodically on SU₂-character varieties

2012/06/12 by Funar, Louis, Marché, Julien
#57M99 #58D29 #58F11 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1206.2541

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 SU₂. Our proof relies on a local description of the latter space around the trivial representation and on the Taylor expansion of trace functions.

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