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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