论文标题
McCool Whitehead类型定理，用于有限生成的$ \ Mathsf {out}（f_n）$的子组
A McCool Whitehead type theorem for finitely generated subgroups of $\mathsf{Out}(F_n)$
论文作者
论文摘要
S. Gersten宣布了一种算法，该算法将两个有限序列$ \ vec k =（k_1，\ dots，k_n）$和$ \ \ vec k'=（k_1'，\ dots，k_n'）$ conjugacy类别的$ f_n $和输出的偶然生成子类别的类别的类别 （1）$ \ MATHSF {YES} $或$ \ MATHSF {no} $，具体取决于\ Mathsf {out}（f_n）$中是否有元素$θ\（f_n）$ （2）$ \ mathsf {out}（f_n）$ fixing $ \ vec k $的子组的有限演示文稿。 S.Kalajdžievski发布了该算法的验证。从Culler-Vogtmann的外部空间的角度来看，我们提出了不同的算法。 新结果包括$ \ mathsf {out}（f_n）$ fixing $ \ vec k $的子组是类型$ \ mathsf {vf} $，这是这些结果，应用程序和统一方法的类似版本。
S. Gersten announced an algorithm that takes as input two finite sequences $\vec K=(K_1,\dots, K_N)$ and $\vec K'=(K_1',\dots, K_N')$ of conjugacy classes of finitely generated subgroups of $F_n$ and outputs: (1) $\mathsf{YES}$ or $\mathsf{NO}$ depending on whether or not there is an element $θ\in \mathsf{Out}(F_n)$ such that $θ(\vec K)=\vec K'$ together with one such $θ$ if it exists and (2) a finite presentation for the subgroup of $\mathsf{Out}(F_n)$ fixing $\vec K$. S. Kalajdžievski published a verification of this algorithm. We present a different algorithm from the point of view of Culler-Vogtmann's Outer space. New results include that the subgroup of $\mathsf{Out}(F_n)$ fixing $\vec K$ is of type $\mathsf{VF}$, an equivariant version of these results, an application, and a unified approach to such questions.
