## About the course

Building on the foundational material from Math 549, we will discuss
several aspects of the geometry and topology of smooth manifolds. The
course will be divided into three roughly equal units focusing on the
following topics:

- Smooth actions and quotients
- Bundles, connections, and curvature
- Symplectic manifolds

## Supplementary texts

Most of the material we will cover can be found in the main textbook (Lee); however, we will occasionally cover material drawn from the supplementary texts listed below. These books may also be useful for students seeking a second exposition of material that is included in the primary text.

- F. Warner,
*Foundations of Differentiable Manifolds and Lie Groups*. (Springer GTM, 1983)
- M. Spivak,
*A Comprehensive Introduction to Differential Geometry*, Volume 1. (Publish or Perish, 1999) (Full text on archive.org)
- R. W. Sharpe,
*Differential Geometry: Cartan's
Generalization of Klein's Erlangen Program*. (Springer GTM, 2000)
- A. Cannas da Silva,
*Lectures on Symplectic Geometry*. (Online lecture notes; also available in Springer LNM series)
- D. McDuff and D. Salamon,
*Introduction to Symplectic Topology*. (Oxford, 1999)