Mapping class group dynamics on Aff(C)-characters

2014/06/29 by Ghazouani, Selim · 1 citation
#Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1406.7489

Abstract

We prove that in genus bigger than 2, the mapping class group action on Aff(ℂ)-characters is ergodic. This implies that almost every representation π₁ S \longrightarrow Aff(ℂ) is the holonomy of a branched affine structure on S, where S is a closed orientable surface of genus g ≥ 2.

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