The first Johnson subgroups act ergodically on SU_2-character varieties

Louis Funar (1) , Julien Marché (2)

1 IF - Institut Fourier
2 CMLS - Centre de Mathématiques Laurent Schwartz

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 SU_2. Our proof relies on a local description of the latter space around the trivial representation and on the Taylor expansion of trace functions.

Domaines: Topologie géométrique [math.GT]; Systèmes dynamiques [math.DS]

Louis Funar, Julien Marché. The first Johnson subgroups act ergodically on SU_2-character varieties. 2012. ⟨hal-00843247⟩