This is a second course in algebraic topology. We will cover cohomology (if not covered in the first semester), homotopy theory, characteristic classes, and possibly spectral sequences if time allows.
Cohomology and Homotopy Theory: A. Hatcher, Algebraic Topology and J. Milnor, Topology from the Differentiable Viewpoint. Characteristic Classes: J. Milnor and W. Stasheff, Characteristic Classes and A. Hatcher, Vector Bundles and K-Theory; Spectral Sequences: A. Hatcher, Spectral Sequences in Algebraic Topology and R. Bott and L. Tu, Differential Forms in Algebraic Topology
Math 540 or equivalent