Mapping class group actions on configuration spaces and the Johnson filtration

Andrea Bianchi, Jeremy Miller, Jennifer C. H. Wilson

Let $F_n({\Sigma }_{g,1})$ denote the configuration space of $n$ ordered points on the surface ${\Sigma }_{g,1}$ and let ${\Gamma }_{g,1}$ denote the mapping class group of ${\Sigma }_{g,1}$. We prove that the ac…