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.

Grading: Homeworks 4/7, Midterm Exam 3/7

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), characteristic classes (Pontrjagin, Euler, Chern).

Textbook: Differential Geometry (Loring Tu). Also recommended is Introduction to Riemannian Manifolds (John Lee), 2nd Ed. for geodesics, and Introduction to Smooth Manifolds (John Lee), 2nd Ed. for vector bundles and Lie groups.

Page maintained by Anil N. Hirani
Last modified: Thu May 9 14:00:50 CDT 2019