Differential Topology

3 credits · Graduate School

Manifolds; submanifolds; tangent and vector bundles. Vector fields and flows, Lie brackets, distributions, and the Frobenius theorem. Sard's theorem; transversality and intersection theory; degree theory and applications. Tensors and differential forms; the exterior derivative; Stokes' theorem and integration; de Rham cohomology. No credit for students who have earned credit for 270. Prerequisite: either 2410, 2600, or 2501, and either 3200, 4220, or 4200. [3] (MNS)