Math 519. Differentiable Manifolds II Instructor Syllabus
The class will meet for three contact hours.
Grading for this course will be determined by the instructor.
Topics to be covered
1. Vector bundles, Principle bundles; connections; parallel transport; Levi-Civita connections; curvature; Chern-Weyl classes.
2. Hodge-DeRham theory.
3. Other possible topics: geometric structures (e.g., Riemannian metrics, symplectic structures), spin geometry, harmonic maps.
Foundations of differentiable manifolds and Lie groups, Frank W. Warner, Springer, 1983.
An Introduction to Differentiable Manifolds, Dennis Barden and Charles B. Thomas, Imperial College Press, 2003.