Mapping class group dynamics on Aff(C)-characters

Abstract

We prove that in genus bigger than $2$, the mapping class group action on $\mathrm{Aff}(\mathbb{C})$-characters is ergodic. This implies that almost every representation ${\pi }_{1}S⟶\mathrm{Aff}(\mathbb{C})$ is the holonomy of a branched affine structure on $S$, where $S$ is a closed orientable surface of genus $g\ge 2$.