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
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, ...)
MTG 6256 (taken Fall 1999) or the equivalent
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