Prof. Paul Gunnells, LGRT 1115L, 545-6009, gunnells at math dot umass dot edu.

- Tuesdays (11.30-12.30)
- Thursdays (12.30-1.30)

Topics in Geometry II follows Math 703 and continues the development of the topology and geometry of differentiable manifolds. Topics include vector bundles, differential forms, tensors, Stokes's theorem, de Rham cohomology, and Riemannian geometry.

The required texts are

- Lee, "Introduction to Smooth Manifolds." 2nd edition.
- Lee, "Riemannian Manifolds: an Introduction to Curvature."

Others that you might find valuable are

- Boothby, "An Introduction to Differentiable Manifolds and Riemannian Geometry"
- Warner, "Foundations of Differentiable Manifolds and Lie Groups"
- Spivak, "Differential Geometry, vol. I"
- Guillemin and Pollack, "Differential Topology."
- Gallot, Hulin, and Lafontaine, "Riemannian Geometry"
- Milnor, "Topology from the differentiable viewpoint"
- Hicks, "Notes on differential geometry"

There will be problem sets assigned during the term. Some problems will be graded, and will count for 25% of your grade. There will also be a midterm and a final exam, which will be worth 30% each. The remaining 15% will be based on course participation.

Please make sure you are using the problems from the second edition of the textbook. The first edition has different problems.

The date and time of the final will be set later in the term.

Revised: Sun Apr 23 15:04:12 EDT 2017

Paul Gunnells

gunnells at math dot umass dot edu