论文标题
右角Artin团体的可升起自动形态
Liftable automorphisms of right-angled Artin groups
论文作者
论文摘要
给定常规覆盖地图$φ：λ\至图的γ$，我们研究了自动形态组的$ \ permatatorName $ \ permatatorName {aut}（aut}（aut}（a_γ）$，右角artin组$a_γ$。该亚组包括所有可以将其提升为$a_λ$的自动形态。我们首先表明$ \ permatatOrname {laut}（φ）$是由劳伦斯基本自动形态的有限子集生成的。 对于子组$ \ operatoTorname {faut}（φ）$的$ \ operatatorName {aut}（a_λ）$，它由$ \ operatatorname {laut}的自动形态升降组成（φ）$ $ \ operatorName {faut}（φ）\ to \ operatotorName {laut}（φ）$由$φ$诱导。然后，我们表明这种同态的内核实际上是Torelli子组$ \ permatatorName {ia}（a_λ）$的子组，并推断出一个简短的精确序列，让人联想到Birman-Hilden理论的结果。
Given a regular covering map $φ:Λ\to Γ$ of graphs, we investigate the subgroup $\operatorname{LAut}(φ)$ of the automorphism group $\operatorname{Aut}(A_Γ)$ of the right-angled Artin group $A_Γ$. This subgroup comprises all automorphisms that can be lifted to automorphisms of $A_Λ$. We first show that $\operatorname{LAut}(φ)$ is generated by a finite subset of Laurence's elementary automorphisms. For the subgroup $\operatorname{FAut}(φ)$ of $\operatorname{Aut}(A_Λ)$, which consists of lifts of automorphisms in $\operatorname{LAut}(φ)$, there exists a natural homomorphism $\operatorname{FAut}(φ)\to\operatorname{LAut}(φ)$ induced by $φ$. We then show that the kernel of this homomorphism is virtually a subgroup of the Torelli subgroup $\operatorname{IA}(A_Λ)$ and deduce a short exact sequence reminiscent of results from the Birman--Hilden theory for surfaces.
