Integrated MSc-PhD Program


KSM4E06: Algebraic Topology-II


Topics covered: Simplicial and singular homology, simplicial homology, singular homology, homotopy invariance, exact sequences and excision, the equivalence of simplicial and singular homology, computations and applications, degree, cellular homology, Mayer-Vietoris sequences, homology with coefficients. Cohomology groups, the universal coefficient theorem, cohomology of spaces, cup product, the cohomology ring, a Kunneth formula, spaces with polynomial cohomology, Poincaré duality, orientations and homology, the duality theorem, connection with cup product, other forms of duality, universal coefficients for homology, the general Kunneth formula.

Suggested texts:

            1. Algebraic Topology by Allen Hatcher
            2. An Introduction to Algebraic Topology by Joseph Rotman
            3. Algebraic Topology: An Introduction by William S. Massey