不动点与Nielsen数

FIXED POINT AND Nielsen NUMBER

通过研究拓扑空间上幂等自映射在基本群上诱导的作用和点同伦,得到与之同伦的,具有较好性质的自映射。并利用自映射这些性质,得到幂等自映射的Nielsen数不超过1的结论。同时亦为高阶同伦群为平凡的拓扑空间上的自映射的Nielsen数的计算提供了一个新思路。

We proof that a self-mapping have preferably characteristic on topological space,is homotopic to power-equate self-mapping by it induces action on the fundamental group of the sapce and point homotopy.By the characteristices,be proof that the Nielsen number of power-equate self-mapping is not more than unit.Atyone time,be give one computing engineers to count the Nielsen number of self-mapping on space,if the higher dimensionality homotopy groups of the space are zero.