Algebraic Topology I

Course content

Fundamental group, Van Kampen’s Theorem, covering spaces. Singular homology: Homotopy invariance, homology long exact sequence, Mayer-Vietoris sequence, excision. Cellular homology. Homology with coefficients. Simplicial homology and the equivalence of simplicial and singular homology. Axioms of homology. Homology and fundamental groups. Simplicial approximation. Applications of homology.