Garrett Nelson

The goal of this talk is to show that subgroups of free groups are free. Wewill introduce concepts from algebraic topology following the proof fromReinhold Baer and Friedrich Levi in 1936. We will overview theconstruction of free groups, the construction of the fundamental group,covering spaces, and linear graphs through definitions and examples. Therelation between covering spaces of a ‘nice’ topological spaceXandsubgroups of the fundamental group ofXwill be highlighted in this talk.Some knowledge of abstract algebra and analysis will be helpful inunderstanding the material covered.