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Non-trivial action of the Johnson filtration on the homology of configuration spaces (2208.01608v1)
Published 2 Aug 2022 in math.GT, math.AT, and math.GN
Abstract: We let the mapping class group $\Gamma_{g,1}$ of a genus $g$ surface $\Sigma_{g,1}$ with one boundary component act on the homology $H_*(F_{n}(\Sigma_{g,1});\mathbb{Q})$ of the $n{th}$ ordered configuration space of the surface. We prove that the action is non-trivial when restricted to the $(n-1){st}$ stage of the Johnson filtration, for all $n\ge 1$ and $g\ge 2$. We deduce an analogous result for closed surfaces.