The fundamental group, covering spaces, core topics in homology and cohomology theory including CW complexes, universal coefficients, and Poincare duality.
At the level of Hatcher, Algebraic Topology
- Singular homology and chain complexes
- Homological algebra, universal coefficients
- CW complexes
- Singular cohomology
- Products and Duality on manifolds
- The fundamental group and Van Kampen’s theorem.
- Covering space and connections with the fundamental group.