PMATH 465
Smooth Manifolds
Fall 2024
Topics
- Smooth manifolds and maps
- Tangent and cotangent bundles
- Vector fields and tensor fields
- Differential forms and Stokes’s theorem
- Integral curves and Lie derivatives
Readings
- Introduction to Smooth Manifolds
Fall 2020 · Geometry of Manifolds
Readings
- Introduction to Smooth Manifolds; Second Edition; by Lee (Springer GTM)
- An Introduction to Differentiable Manifolds and Riemannian Geometry; by Boothby (Academic Press) I will not prepare my lectures by following any particular book exactly. This is a good thing for you, since by viewing the lectures and by also reading various books you will have multiple points of view on the topics, which will make it easier to understand. The best way to learn is to read books, view the lectures, and then read books again. (And then read books a third or fourth time if necessary.)
- There is no required textbook. However, there are many excellent books that cover this material. Here are two useful books, which will both be on reserve at the Davis library:
Sources
- Course catalogue ↗2026–2027
- course_outline ↗Fall 2024
- course_outline ↗Fall 2020
- Fall 2024 outline. The textbook is explicitly required.
- Official public PDF outline or course description. Materials and topic extracts may be partial; consult the linked source for the full list.