Fundamental Groups (Hatcher 1.1)

This talk was given in preparation for the UCLA geometry/topology qualifying exam, specifically the algebraic topology portion. It aims to define fundamental groups, find the fundamental group of the circle, and show some applications of fundamental groups. Basically all of the material is taken from Allen Hatcher's "Algebraic Topology" section 1.1.

The notes for this video, which are perhaps more useful than the video itself, can be found at

The video showing that the torus is abelian can be found at

Finally, this video is intended to be the first/second in a series of videos outlining the important portions of algebraic topology needed for the qualifying exam. The link to the full playlist can be found at