## 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