Math 550: Differentiable Manifolds II

David Dumas

University of Illinois at Chicago
Fall 2014

[a 1-manifold that looks like a 2-manifold]

General information

Instructor David Dumas (
Lectures MWF 10am in Taft Hall 309
CRN 37063
Office hours Monday and Friday 2-3pm
Texts M. Lee, Introduction to Smooth Manifolds. (Springer GTM, 2012)
    → Available online through the UIC library
M. Spivak, A Comprehensive Introduction to Differential Geometry, Volume 1. (Publish or Perish, 1999)
F. Warner, Foundations of Differentiable Manifolds and Lie Groups. (Springer GTM, 1983)
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)

Course description

Building on the foundational material from Math 549, we will discuss several aspects of the geometry and topology of smooth manifolds. Topics will include de Rham theory, distributions and foliations, Lie groups, Lie algebras, vector bundles, principal bundles, and symplectic geometry.

A more detailed topic outline is provided in the course syllabus. The topics may be adjusted to account for time constraints and for the background and preferences of the students.

Course materials

Links and resources

Here we collect citations for further reading about course material (beyond the course texts) and links to relevant online materials.
Up: Home page of David Dumas