This course is a continuation of Math 540 Algebraic Topology I. The main topics of this course are cohomology theory and homotopy theory, with the following specific topics: cohomology groups, cup product, Poincare duality, homotopy groups, Whitehead theorem, Hurewicz theorem, fiber bundles, etc. Applications of algebraic topology to low-dimensional topology will also be given.
Allen Hatcher, Algebraic Topology
Math 540 Introduction to Algebraic Topology II