This course is an introduction to Algebraic Topology. Its main topic is the study of homology groups of topological spaces. These homology groups provide algebraic invariants of topological spaces which can be computed in many examples of interest.
In the first part of the course we will construct the singular homology groups of topological spaces and establish their basic properties, such as homotopy invariance and long exact sequences. In the second part of the course we will introduce CW-complexes. These
provide a useful class of topological spaces with favorable properties, and we will explain how the homology of CW-complexes can be computed using cellular homology. If time allows, we may also discuss additional topics such as singular cohomology or basic
concepts of homotopy theory.
- A course in point-set topology.
- The Intensive course on Categories and Modules or equivalent previous knowledge.
- Docent: Steffen Sagave