Differentiable Manifolds II

MATH 519, Spring 2019

447 Altgeld Hall, TR 11:00 AM

University of Illinois at Urbana-Champaign, Department of Mathematics

Instructor: Anil Hirani (email), Altgeld Hall Room 375

Office Hours: Anil Hirani: Wednesday 1:00 -- 2:00 PM and by appointment, Room 375 Altgeld Hall.

All course grades, announcements and homeworks will be posted on Moodle.

There will be approximately 11-13 homeworks due every Thursday each with perhaps 2 exercises, one take-home midterm exam and one in-class final.

Grading: Homeworks 40%, Midterm Exam 30%, Final Exam 30%

Topics: Riemannian manifolds, vector bundles, Lie groups, connections and curvature, Gauss' Theorema Egregium, Gauss-Bonnet Theorem, geodesics, exponential map, some tools from algebra (tensor products, operations on vector bundles, vector-valued forms), characteristic classes (Pontrjagin, Euler, Chern).

Textbook: Differential Geometry (Loring Tu). Also recommended is Riemannian Geometry (Gallot, Hulin, Lafontaine).

Page maintained by Anil N. Hirani
Last modified: Tue Jan 15 14:19:53 CST 2019