Plan

The curriculum will be drawn from chapters 3 and 4 of Allen Hatcher's textbook "Algebraic Topology", covering Cohomology and Homotopy Theory.  The transition from homology to cohomology leads to a (cup) product structure that in the case of manifolds satisfies a (Poincar¨¦) duality theorem, represents cohomology classes by maps to (Eilenberg-MacLane) spaces, and leads to a classification of homotopy types by (Postnikov) k-invariants.  We should cover most of sections 3.1, 3.2, 3.3 and large parts of sections 4.1, 4.2 and 4.3.  We may sometimes refer to the results in the appendix on cell complexes.