论文标题
关于Nielsen Zeta函数在solvmanifolds上的地图的合理性
On the rationality of the Nielsen zeta function for maps on solvmanifolds
论文作者
论文摘要
在[3,9]中，如果$ f $是类型（R）的Infra-Solvmanifold的自图，则证明Nielsen Zeta函数$ n_f（z）$是合理的。但是，仍然未知$ n_f（z）$对于solvmanifolds上的自图是否合理。在本文中，我们证明$ n_f（z）$是合理的，如果$ f $是尺寸$ \ leq 5 $的（紧凑）solvmanifold的自图。在任何维度上，我们还表明，如果$ n_f（z）$是$ f $是$ {\ cal nr} $ - solvmanifold或solvmanifold或具有基本形式$ {\ mathbb z}^n \ rtimes {\ mathbb z} $的基本组的solvmanifold，则是合理的。
In [3,9], the Nielsen zeta function $N_f(z)$ has been shown to be rational if $f$ is a self-map of an infra-solvmanifold of type (R). It is, however, still unknown whether $N_f(z)$ is rational for self-maps on solvmanifolds. In this paper, we prove that $N_f(z)$ is rational if $f$ is a self-map of a (compact) solvmanifold of dimension $\leq 5$. In any dimension, we show additionally that $N_f(z)$ is rational if $f$ is a self-map of an ${\cal NR}$-solvmanifold or a solvmanifold with fundamental group of the form ${\mathbb Z}^n\rtimes{\mathbb Z}$.
