论文标题
$ k（π，1）$猜想和相对超大的Artin组的阳性双曲线
The $K(π,1)$ conjecture and acylindrical hyperbolicity for relatively extra-large Artin groups
论文作者
论文摘要
令$a_γ$成为一个具有定义图$γ$的Artin组。我们介绍了$a_γ$的概念，相对于一个任意抛物线子组的家族而言。相对于两个抛物线亚组，这概括了$a_γ$的相关概念，其中一个总是很大。在这种新条件下，我们表明$a_γ$在每个杰出的子组都这样的时满足$ k（π，1）$猜想。此外，我们表明$a_γ$仅在轻度条件下是酰基柔毛的。
Let $A_Γ$ be an Artin group with defining graph $Γ$. We introduce the notion of $A_Γ$ being extra-large relative to a family of arbitrary parabolic subgroups. This generalizes a related notion of $A_Γ$ being extra-large relative to two parabolic subgroups, one of which is always large type. Under this new condition, we show that $A_Γ$ satisfies the $K(π,1)$ conjecture whenever each of the distinguished subgroups do. In addition, we show that $A_Γ$ is acylindrically hyperbolic under only mild conditions.
