Surface configuration kernels

Let ${\mathrm{\Sigma }}_{g,\ast }$ be a once-punctured oriented surface of genus $g$. We study the action of the mapping class group ${\mathrm{\Gamma }}_{g,\ast }$ on the $n^{th}$ rational cohomology of the configuration space ${\text{Conf}}_n({\mathrm{\Sigma }}_{g,\ast })$ of injections $\{1,\dots ,n\}\hookrightarrow {\mathrm{\Sigma }}_{g,\ast }$, and compare the kernel $J_{g,\ast }^{cfg}(n)$ of this action with the $n^{th}$ Johnson subgroup $J_{g,\ast }(n)$. We find high-rank abelian subgroups in the quotient $J_{g,\ast }^{cfg}(n)\mathrm{/}{J}_{g,\ast }(n)$ arising from the higher Johnson images and from symplectic representation theory. In particular we refute a conjecture due to Bianchi–Miller–Wilson.