MTH 7375 - Section 2 - Topics in Topology: Fiber bundles and characteristic classes
Course description: Introduces fiber bundles and characteristic classes. Topics include the construction of universal bundles, homotopy classification of principal bundles, bundles over spheres, cohomology of classifying spaces, Stiefel-Whitney classes, Gysin and Wang sequences, Thom isomorphism, Euler class, obstructions, Chern classes, and Pontrjagin classes.
References:
Required: The topology of fiber bundles – Lecture notes, Ralph Cohen. Available at https://math.stanford.edu/~ralph/fiber.pdf
Optional: Fibre Bundles, Dave Husemoller
Optional: Characteristic classes, John Milnor and James Stasheff
Optional: From calculus to cohomology: De Rham cohomology and characteristic classes, Ib Madsen and Jxrgen Tornehave
Syllabus (pdf)
Lectures: