Playlist:    • Algebraic Topology  

We give a brief recap of homology and then show how dualizing the chain complex by Hom(--,Z) gives a cochain complex with coboundary maps that we use to calculate cohomology. We show that for finitely generated chain groups, we can calculate the cohomology in terms of the homology groups. Then we dualize with other coefficient groups G and discuss the universal coefficient theorem for cohomology.


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/...