Mth 636 Algebraic Topology III

Topics from singular and simplicial homology and cohomology theories, fundamental group and covering spaces, CW complexes and elements of homotopy theory, algebraic theory of manifolds, introduction to differential topology and vector bundles, applications. This is the third course in a sequence of three: Mth 634, Mth 635, and Mth 636 which must be taken in sequence. Expected preparation: Mth 435/Mth 535 and Mth 444/Mth 544.