论文标题
拉格斯的外太空
Outer space for RAAGs
论文作者
论文摘要
对于任何右角artin组$a_γ$，我们构建一个有限维空间$ \ MATHCAL {o}_γ$，$a_γ$的外部自动形态的$ \ text {out}（a_γ）$在其上具有有限点稳定器。我们证明$ \ Mathcal {o}_γ$是可签约的，因此商是$ \ text {out}（a_γ）$的合理分类空间。空间$ \ MATHCAL {O}_γ$将lattices的对称空间的特征$ \ Mathbb {r}^n $与免费组的外在空间$ f_n $一起。 $ \ MATHCAL {O}_γ$中的点是本地CAT（0）公制空间，它们是同型（但不是等速度）的某些本地CAT（0）Cube（0）Cube Complextes，其标志着其基本组的同构和$A_γ$。
For any right-angled Artin group $A_Γ$ we construct a finite-dimensional space $\mathcal{O}_Γ$ on which the group $\text{Out}(A_Γ)$ of outer automorphisms of $A_Γ$ acts with finite point stabilizers. We prove that $\mathcal{O}_Γ$ is contractible, so that the quotient is a rational classifying space for $\text{Out}(A_Γ)$. The space $\mathcal{O}_Γ$ blends features of the symmetric space of lattices in $\mathbb{R}^n$ with those of Outer space for the free group $F_n$. Points in $\mathcal{O}_Γ$ are locally CAT(0) metric spaces that are homeomorphic (but not isometric) to certain locally CAT(0) cube complexes, marked by an isomorphism of their fundamental group with $A_Γ$.
