论文标题
扭曲的共轭和相称性不变性
Twisted conjugacy and commensurability invariance
论文作者
论文摘要
如果每个自动形态$φ\ in {\ rm aut}（g）$，则$ g $据说具有属性$ r _ {\ infty} $，这是$φ$ twisted的共轭类的基数是无限的。许多类别都有这样的属性。但是，很少有人以$ r _ {\ infty} $为{\ it几何}的示例，即，如果$ g $具有属性$ r _ {\ infty} $，则任何Quasi iSometric to $ g $也具有$ g $的quasi imemetric，也具有属性$ r _ {\ infty} $。在本文中，我们举例说明了$ r _ {\ infty} $的群体和条件。主要工具是使用Bieri-Neumann-Strebel不变式。
A group $G$ is said to have property $R_{\infty}$ if for every automorphism $φ\in {\rm Aut}(G)$, the cardinality of the set of $φ$-twisted conjugacy classes is infinite. Many classes of groups are known to have such property. However, very few examples are known for which $R_{\infty}$ is {\it geometric}, i.e., if $G$ has property $R_{\infty}$ then any group quasi-isometric to $G$ also has property $R_{\infty}$. In this paper, we give examples of groups and conditions under which $R_{\infty}$ is preserved under commensurability. The main tool is to employ the Bieri-Neumann-Strebel invariant.
