论文标题
绘制班级组的双约翰逊过滤
Double Johnson filtrations for mapping class groups
论文作者
论文摘要
我们首先开发了约翰逊过滤和约翰逊同构的一般理论，该理论是在另一组$ k $上作用的$ g $，该$ k $配备了“良好”订购的交换性单体索引的过滤。然后，将其专门化为单型是非负整数上的添加剂单体$ \ mathbb {n}^2 $，我们获得了双重约翰逊过滤和同质形态的理论。我们将此理论应用于一个$ \σ_{g，1} $的映射类$ \ MATHCAL {M} $，其中一个边界组件，配备了正常子组$ \ bar {x} $，$ \ bar {y} $ $π_1（$π_1（y} $π_1）我们还考虑了$ g $是免费组的自动形态组的情况。
We first develop a general theory of Johnson filtrations and Johnson homomorphisms for a group $G$ acting on another group $K$ equipped with a filtration indexed by a "good" ordered commutative monoid. Then, specializing it to the case where the monoid is the additive monoid $\mathbb{N}^2$ of pairs on nonnegative integers, we obtain a theory of double Johnson filtrations and homomorphisms. We apply this theory to the mapping class group $\mathcal{M}$ of a surface $Σ_{g,1}$ with one boundary component, equipped with the normal subgroups $\bar{X}$, $\bar{Y}$ of $π_1(Σ_{g,1})$ associated to a standard Heegaard splitting of the $3$-sphere. We also consider the case where the group $G$ is the automorphism group of a free group.
