Igor Caetano: Homology and Cohomology Theories: An Algebraic Approach

Abstract

 I will talk about Eilenberg's axioms on homology theories, go through the definition of homology for CW-Complexes and do a few concrete computations such as computing the homology of quotients and the sphere. In the end, I want to finish off by going through a slick proof of the Jordan Curve theorem using homology.