Algebraic Topology 10: Simplicial Homology

Playlist:    • Algebraic Topology  

We discuss higher dimensional homotopy groups, highlighting the difficulty of calculating them for even spheres, motivating the shift to homology which is easier to calculate. Then we define simplicial complexes, and the more general delta-complexes, and show how we use these to create a chain complex with a boundary operating relating the abelian groups with basis the n-simplicies. We give several examples of calculating simplicial homology, including the disk, circle, sphere, and torus.

Presented by Anthony Bosman, PhD.
Learn more about math at Andrews University: https://www.andrews.edu/cas/math/
In this course we are following Hatcher, Algebraic Topology: https://pi.math.cornell.edu/~hatcher/...