On the self-intersections of curves deep in the lower central series of a surface group
On the self-intersections of curves deep in the lower central series of a surface group
复制标题
曲面群下中心系列深处曲线的自交
DOI：
--
复制
发表时间：
2009
期刊：
影响因子：
--
通讯作者：
Andrew Putman
中科院分区：
文献类型：
--
作者：
Justin Malestein;Andrew Putman
我们给各种估计的最小数目的自交的一个非平凡元素的第k项的下中心系列和衍生系列的基本群的表面。作为应用，我们得到了闭曲面的自由群和基本群是剩余幂零的一个新的拓扑证明。沿着的方式，我们证明了一个非阿贝尔自由群的下中心系列的第k项的非平凡元素必须有一个自由生成集的字长至少为k。
We give various estimates of the minimal number of self-intersections of a nontrivial element of the kth term of the lower central series and derived series of the fundamental group of a surface. As an application, we obtain a new topological proof of the fact that free groups and fundamental groups of closed surfaces are residually nilpotent. Along the way, we prove that a nontrivial element of the kth term of the lower central series of a nonabelian free group has to have word length at least k in a free generating set.