MATH 652: Differentiable Manifolds I (Fall 2005)

Instructor: James West

Meeting Time & Room

Manifolds and Differentiable maps. Tangent vectors and Tangent Bundles. Submanifolds, normal bundles, and tubular neighborhoods. Vector fields, flows, and Frobenius' Integrability Theorem. Riemannian metrics, parallel transport, curvature, and geodesics. Tensors, exterior derivatives, and Stokes' theorem. Should time permit, other topics such as transversality, Morse theory, or de Rham cohomology will be introduced.

Last modified: April 4, 2005