Algebraic Topology Homology:A review of simplicial homology, Singular homology, Excision, Mayer- Vietoris theorem, CW-complexes and Cellular homology, Classical Applications including the Jordan Curve Theorem. Cohomology:Cohomology groups, Universal coefficient theorems, Cup products, Kunneth formula, Orientation on manifolds, Poincare duality, introduction to smooth manifolds and de Rham cohomology.
Books
- Hatcher, A., Algebraic Topology, Cambridge Univ. Press, 2002 (Indian edition available)
- Bredon, G.E., Topology and Geometry, Springer-Verlag New York, 1993 (Indian edition available)