论文标题
右角Artin组的自动形态群的算术商
Arithmetic Quotients of the Automorphism Group of a Right-Angled Artin Group
论文作者
论文摘要
以前是Grunewald and Lubotzky表明的，免费组的自动形态组，$ \ text {aut}（f_n）$，具有大量的虚拟算术商。 Looijenga和Grunewald，Larsen，Lubotzky和Malestein证明了地图班级组的类似结果。在本文中，我们证明了一个右角ARTIN组的自动形态群的结果，用于大量定义图。作为我们方法的推论，我们生成了$ \ text {aut}（aut}（f_n）$的新的虚拟算术商，$ n \ geq 4 $，其中所有转移的$ k $ th powers y th y ther the ther the powers of the ther the powers of All Transvections Act to to Bive of to Bive to to Bive of to to the of。因此，对于某些$ k $的值，我们推断出$ \ text {aut}（f_n）$的商的商组由$ k $ th thrantvections生成的子组包含nonabelian免费组。这扩展了马拉斯坦和普特曼以及布里森和沃格特曼的结果。
It was previously shown by Grunewald and Lubotzky that the automorphism group of a free group, $\text{Aut}(F_n)$, has a large collection of virtual arithmetic quotients. Analogous results were proved for the mapping class group by Looijenga and by Grunewald, Larsen, Lubotzky, and Malestein. In this paper, we prove analogous results for the automorphism group of a right-angled Artin group for a large collection of defining graphs. As a corollary of our methods we produce new virtual arithmetic quotients of $\text{Aut}(F_n)$ for $n \geq 4$ where $k$th powers of all transvections act trivially for some fixed $k$. Thus, for some values of $k$, we deduce that the quotient of $\text{Aut}(F_n)$ by the subgroup generated by $k$th powers of transvections contains nonabelian free groups. This expands on results of Malestein and Putman and of Bridson and Vogtmann.
