Cornell Math - MATH 652, Fall 2005
MATH 652: Differentiable Manifolds I (Fall 2005)
Instructor: James West
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.