Topology
After introducing metric and general topological spaces, the emphasis will be on the algebraic topology of manifolds and cell complexes. Elements of algebraic topology to be covered include fundamental groups and covering spaces, homotopy and the degree of maps and its applications. Some differential topology will be introduced including transversality and intersection theory. Some examples will be taken from knot theory. Homology and cohomology from simplicial, singular, cellular, axiomatic and differential form viewpoints. Axiomatic characterizations and applications to geometrical problems of embedding and fixed points. Manifolds and Poincare duality. Products and ring structures. Vector bundles, tangent bundles, De Rham cohomology and differential forms.
