Covering Spaces and Fundamental Groups - Algebraic Topology Lecture 28

Explore covering spaces and fundamental groups in this 47-minute lecture from the Algebraic Topology series. Examine examples of covering spaces for the torus and two-holed torus, then delve into the relationship between fundamental groups of covering spaces and base spaces under covering maps. Learn about the Lifting Path lemma and Lifting Homotopy lemma, and discover how the fundamental group of a covering space can be viewed as a subgroup of the base space's fundamental group. Gain insights into studying covering spaces by analyzing subgroups of the fundamental group of the base space.