Representations of surface groups with universally finite mapping class group orbit

Brian Lawrence, Daniel Litt

Let ${\Sigma }_{g,n}$ be the orientable genus $g$ surface with $n$ punctures, where $2-2g-n<0$. Let $$\rho :{\pi }_1({\Sigma }_{g,n})\to G{L}_m(\mathbb{C})$$ be a representation. Suppose that for each finit…