2017/06/29 by Gongping Niu, Niu, Gongping
Mathematics · #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric and Algebraic Topology #math.AT
paper · pdf · doi:10.48550/arxiv.1706.09594
In the content, I study the finitely generated free groups and the subgroups of it. In the appendix A, I review the free groups and coversing spaces. In the appendix B, I prove the Nielsen-Index theorem
arxiv created 2017/06/29 · openalex publication_date 2017/06/29 · arxiv updated 2017/06/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Free groups have many applications in Algebraic Topology. In this paper I specifically study the finitely generated free groups by using the covering spaces and fundamental groups. By the Van Kampen's theorem, we have a famous fact that the fundamental group of a wedge sum of circles is a free group. Therefore, to study free groups, we could try to figure out the covering spaces of the wedge sum of circles. And in the appendix B, I prove the Nielsen-Schreier theorem which I will use this to study finitely index subgroups of a finitely generated free group.