论文标题
测量无转发的非直角ARTIN组的等效分类
Measure equivalence classification of transvection-free right-angled Artin groups
论文作者
论文摘要
我们证明，如果两个无反射的右角artin组是等效的，那么它们具有同构延伸图。结果，当且仅当它们是同构时，两个具有有限外部自动构成组的右角aRTIN组是等效的。这匹配了准时分类。 然而，与准偶像法问题相反，我们观察到，没有两个原因，在最强的含义上，没有直角的Artin组是衡量等效性的超级精神，原因有两个。首先，右角Artin组$ g $始终是相当于在同一定义图上无限可计式组的任何图形产品。其次，当$ g $是nonabelian时，$ g $的萨尔维蒂综合体的通用封面的自动形态群总是包含无限生成的（非均匀）晶格。
We prove that if two transvection-free right-angled Artin groups are measure equivalent, then they have isomorphic extension graphs. As a consequence, two right-angled Artin groups with finite outer automorphism groups are measure equivalent if and only if they are isomorphic. This matches the quasi-isometry classification. However, in contrast with the quasi-isometry question, we observe that no right-angled Artin group is superrigid for measure equivalence in the strongest possible sense, for two reasons. First, a right-angled Artin group $G$ is always measure equivalent to any graph product of infinite countable amenable groups over the same defining graph. Second, when $G$ is nonabelian, the automorphism group of the universal cover of the Salvetti complex of $G$ always contains infinitely generated (non-uniform) lattices.
