论文标题
$ r_ \ infty $ - 右角artin群体
The $R_\infty$-property for right-angled Artin groups
论文作者
论文摘要
给定一个$ g $的组$ g $和一个$ g $的$φ$，如果$ x = gyφ（g）^gyφ（g）^{ - 1} $对于某些$ g \ in g $，则两个元素$ x，y \ in g $ in G $。等价类的数量是$φ$的reidemeister number $ r（φ）$，如果$ r（φ）= \ infty $的所有自动形态$ $ g $，则$ g $，据说$ r_ \ r_ \ infty $ property。 有限的简单图$γ$产生了直角Artin $a_γ$，它作为发电机的顶点$γ$，并且作为关系$ vw = wv $，并且仅当$ v $ and $ w $以$γ$中的优势加入。我们猜想所有非亚伯利亚的右角artin群体都有$ r_ \ infty $ - property，并证明了几个右角Artin群体子类的猜想。
Given a group $G$ and an automorphism $φ$ of $G$, two elements $x, y \in G$ are said to be $φ$-conjugate if $x = g y φ(g)^{-1}$ for some $g \in G$. The number of equivalence classes is the Reidemeister number $R(φ)$ of $φ$, and if $R(φ) = \infty$ for all automorphisms of $G$, then $G$ is said to have the $R_\infty$-property. A finite simple graph $Γ$ gives rise to the right-angled Artin group $A_Γ$, which has as generators the vertices of $Γ$ and as relations $vw = wv$ if and only if $v$ and $w$ are joined by an edge in $Γ$. We conjecture that all non-abelian right-angled Artin groups have the $R_\infty$-property and prove this conjecture for several subclasses of right-angled Artin groups.
