论文标题
Lagrangian的痕迹，用于Johnson滤波器组的过滤
Lagrangian traces for the Johnson filtration of the handlebody group
论文作者
论文摘要
我们将类似痕量的操作员定义在由$σ$的第一个同源性组$ h $生成的自由谎言代数的衍生空间的子空间。该定义取决于$ h $的Lagrangian的选择，我们将这些操作员称为\ emph {lagrangian traces}。我们假设$σ$是带有第一同源性组$ h'$的手柄的边界，我们证明了与lagrangian $ \ operatotorname {ker}相对应的拉格朗日痕迹（h \ rightarrow h'）$消失了约翰逊·菲尔特（Johnson Filetration）的约翰逊（Johnson）元素的图像，以扩展了约翰逊（Johnson）档案范围的elemphistration。
We define trace-like operators on a subspace of the space of derivations of the free Lie algebra generated by the first homology group $H$ of a surface $Σ$. This definition depends on the choice of a Lagrangian of $H$, and we call these operators the \emph{Lagrangian traces}. We suppose that $Σ$ is the boundary of a handlebody with first homology group $H'$, and we show that the Lagrangian traces corresponding to the Lagrangian $\operatorname{Ker} (H \rightarrow H')$ vanish on the image by the Johnson homomorphisms of the elements of the Johnson filtration that extend to the handlebody.
