广义Lefschetz数的粘接公式的应用

Application Of the Pushout Formula of Generalized Lefschetz Number

本文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,使用广义Lefschetz数的粘接公式,得到幂等自映射的Nielsen数不超过1的结论。

A self-mapping having preferably characteristic on topological space is obtained and is homotopic to power-equate self-mapping based on the inducing action on the fundamental group of the space and the point homotopy.By using the characteristic and pushout formula of generalized Lefschetz number,we prove that the Nielsen number of power-equate self-mapping is not more than unit.