**Course:**Differentiable Manifolds II, Math 519, Section M1

**Time:** MWF 11:00--11:50 am.

**Location:** 447 Altgeld Hall

**Instructor:** Chris Leininger

**Phone:** 265-6763

**Email:** clein (at) math.uiuc.edu

**Office:** 265 Altgeld Hall

**Office hours:** TBA

**Text:**
*A Comprehensive Introduction to Differential Geometry, Volume II*, Michael Spivak

*Foundations of Differentiable Manifolds and Lie Groups*, Frank Warner.

*Lecture Notes by Victor Guillemin*, Available from MIT's open courseware here

*Lecture Notes by Chris Wendl*.

*Differential Forms in Algebraic Topology*, R. Bott and L. Tu.

The books will be put on reserve in the library. The lectures will be mostly self contained, with references to
the texts for some proofs.

**Homework:** This will be assigned periodically throughout the semester, but not collected.

**Grading:** Grades are based entirely on class participation.

**Syllabus:** Lie groups, vector bundles, principal bundles, connections, curvature, DeRham and Cech cohomology,
Laplace operator, harmonic forms, and spectral theory.

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