## 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