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arXiv · 1706.09594

A Study of finitely generated Free Groups via the Fundamental Groups

Gongping Niu
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Abstract

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.

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Gongping Niu. 2017-06-29. A Study of finitely generated Free Groups via the Fundamental Groups. https://arxiv.org/abs/1706.09594

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