Starting in the academic year 2018-19, Math 761 will usually be offered in the spring semester.
Lu Wang, Fall 2016/2017:
- Introduction to Smooth Manifolds, by John M. Lee.
- Foundations of Differentiable Manifolds and Lie Groups, by Frank Warner.
- A Comprehensive Introduction to Differential Geometry, Volume I, by Michael Sprivak.
- Differentiable manifold, differential map.
- Tangent space, vector bundle.
- Immersion and embedding.
- Vector field, Lie derivative.
- Frobenius Theorem.
- Tensor and exterior algebra.
- Integration, Stokes' Theorem.
- De Rham cohomology, Poincare Lemma.
- Sard's Theorem, degree of a map.
- Mayer-Vietoris sequence for cohomology, Euler characteristic, triangulations, if time pertmitted.