Basic Topology II

Basic Topology II (Spring Semester) – 60440

1. Homology: singular homology, the Eilenberg-Steenrod axioms, homology group of spheres, the degree of a map between spheres, homology calculations via CW complexes, proof of homotopy invariance, proof of excision, universal coefficient and Kunneth Theorem.
2. Cohomology: the cup product, the cohomology ring of projective spaces.
3. Poincare duality.

Reference

• Hatcher, Algebraic Topology