Step 31 of 37
Uses algebra to tell spaces apart.
Topics, in order
- Fundamental group and van Kampen's theorem
- Covering spaces
- Simplicial and singular homology
- Exact sequences and Mayer–Vietoris
- Cohomology and the cup product
- Poincaré duality
Learn from
- Hatcher, Algebraic Topology (free online)
Move on when
You can compute the homology of a sphere, a torus, and projective space.