Abstract

The main goal of this basic notions seminar is to introduce the audience to the core idea(s) of (co-)homology: To demystify the concept, we will begin with a motivational section, foreshadowing the homological origins of the well-known Poincaré Lemma and the (finite-dim.) Mountain Pass Lemma. Then, we will introduce the (co-)homology theory via general (co-)chain complexes. Next, we will take a look at how to obtain different (co-)chain complexes from various (co-)homology theories yield, and we will try to generate some intuitive understanding of these different theories. At last, we will revisit the examples from the motivational section.