Fiber Bundles and Cobordism

Possible topics: principal bundles, vector bundles, classifying spaces. Connections on bundles, curvature. Topology of gauge groups and gauge equivalence classes of connections. Characteristic classes and K-theory, including Bott periodicity, algebraic K-theory, and indices of elliptic operators. Spectral sequences of Atiyah-Hirzebruch, Serre, and Adams. Cobordism theory, Pontryagin-Thom theorem, calculation of unoriented and complex cobordism. May be repeated for credit up to 6 total units. NOTE: Undergraduates and Masters students who wish to enroll must fill out a Request for Review form: https://forms.gle/v5RojToYzmYxGvKc7 ; Your request will be reviewed by faculty and you'll be notified if you are granted permission to enroll.