Course Announcement

Differential Geometry II : MTG 6257
Spring 2000
New time and room as of Wed. Jan. 19:
MWF 5th period (3:00-3:50), Little 368

Instructor: David Groisser (groisser@math.ufl.edu)

Course summary. This is the second semester of a year-long graduate sequence introduces the tools of differential geometry and differential topology. Topics for MTG6257 will include:
Parallel transport and holonomy.

Geometry of surfaces in R3; Gauss-Bonnet Theorem

Further topics in Riemannian geometry (geodesics, Jacobi fields, Hopf-Rinow Theorem)

Lie groups

Connnections on principal fiber bundles and associated vector bundles.

Curvature and characteristic classes

Gauge theory and the Yang-Mills equations

If time permits, some of the following topics may also be covered:

Symplectic geometry and the geometry of classical mechanics

Curvature comparison theorems in Riemannian geometry.

Spin bundles, Spinc bundles, Dirac operators, and the Seiberg-Witten equations

Complex and Kaehler manifolds

Sard's theorem and some applications

Selected topics in differential topology (transversality, Poincare-Hopf Theorem, degree theory, embedding theorems, ...)



Prerequisite for MTG 6257

Required texts for MTG 6257

None, since I will not be following any textbook very closely for more than a few weeks at a time. However, new students should read the discussion of texts on the MTG 6256 course announcement page.
Last update made by D. Groisser Fri Jan 14 15:12:40 EST 2000