论文标题
与载体的基本平坦歧管基本组的基本属的属属
Profinite genus of fundamental groups of compact flat manifolds with holonomy group of prime order
论文作者
论文摘要
在本文中，我们计算了与Prime Order的Holomany Group a $ n $ dimensional comptact flat歧管$ x $的基本组的属性属。结果，我们证明，如果$ n \ leq 21 $，则$ x $是在其基本组的所有$ n $二维紧凑型平面流形中确定的。此外，我们表征了$ x $的基本群体的同构阶段，就其自治组的代表属而言。
In this article we calculate the profinite genus of the fundamental group of a $n$-dimensional compact flat manifold $X$ with holonomy group of prime order. As consequence, we prove that if $n\leq 21$, then $X$ is determined among all $n$-dimensional compact flat manifolds by the profinite completion of its fundamental group. Furthermore, we characterize the isomorphism class of profinite completion of the fundamental group of $X$ in terms of the representation genus of its holonomy group.
