论文标题
偏斜$γ$ - 复合物的等轴测组
Isometry groups of skewed $Γ$-complexes
论文作者
论文摘要
令$a_γ$为一个直角的Artin组。 charney，vogtmann和作者为$ \ text {out}（a_γ）构建了一个外层空间，$ clemalkize $ \ cv_n $ for $ \ text {out}（out}（f_n）$和对称空间$ \ text $ \ text {sl} _n（sl} _n（\ mathbb {r}） $ \ text {gl} _n（\ mathbb {z}）$。该空间中的点是对的等效类$（x，ρ）$，其中$ρ\ colon x \ rightarrow \ mathbb {s}_γ$是从$ x $到salvetti complect $ x $ to salvetti complect $ \ mathbb {s}}_γ$和$ x $的同质等价。在本说明中，我们表明，偏斜的$γ$ - 复合物的任何等轴测图都与身份相均匀，都在于$ \ text {isom}（x）$的身份分量。作为推论，我们证明$ \ text {isom}（x）$的路径组件组是有限的，并注入$ \ text {out}（a_γ）$。
Let $A_Γ$ be a right-angled Artin group. Charney, Vogtmann and the author constructed an outer space for $\text{Out}(A_Γ)$ generalizing both $CV_n$ for $\text{Out}(F_n)$ and the symmetric space $\text{SL}_n(\mathbb{R})/\text{SO}_n(\mathbb{R})$ for $\text{GL}_n(\mathbb{Z})$. Points in this space are equivalence classes of pairs $(X,ρ)$ where $ρ\colon X\rightarrow \mathbb{S}_Γ$ is a homotopy equivalence from $X$ to the Salvetti complex $\mathbb{S}_Γ$ and $X$ is a locally CAT(0) space called a skewed $Γ$-complex. In this note we show that any isometry of a skewed $Γ$-complex which is homotopic to the identity lies in the identity component of $\text{Isom}(X)$. As a corollary, we prove that the group of path components of $\text{Isom}(X)$ is finite and injects into $\text{Out}(A_Γ)$.
