论文标题
约翰逊过滤对配置空间同源的非平凡动作
Non-trivial action of the Johnson filtration on the homology of configuration spaces
论文作者
论文摘要
我们让映射类$γ_{g，1} $的$ g $表面$ g $ c $σ_{g，1} $带有一个边界组件在同源性$ h _**（f_ {n}（σ_{n}（σ_{g，1}}）; \ mathbb {q}）;我们证明，当所有$ n \ ge 1 $和$ g \ ge 2 $限制在约翰逊过滤的$（n-1）^{st} $阶段时，该动作是不平凡的。我们推断出封闭表面的类似结果。
We let the mapping class group $Γ_{g,1}$ of a genus $g$ surface $Σ_{g,1}$ with one boundary component act on the homology $H_*(F_{n}(Σ_{g,1});\mathbb{Q})$ 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.
