Introduction to Differentiable Manifolds

Graduate / Professional

This is an introduction to the general theory of smooth manifolds, developing tools for use elsewhere in mathematics. A rough plan of topics (with the later ones as time permits) includes (1) manifolds, tangent spaces, vector fields and flows; (2) natural examples, submanifolds, quotient manifolds, fibrations, foliations; (3) vector and tensor bundles, differential forms; (4) Lie derivatives, Lie algebras and groups; (5) embedding, immersions and transversality; and (6) Sard’s theorem, degree and intersection. Prerequisites: Multivariable calculus ( MATH 1200 or 3020 ), linear algebra ( MATH 2250 or 2260 ), and topology ( MATH 4300 ). TTh 2:35pm-3:50pm