Math 519: Differentiable Manifolds II
Basic Information
 Instructor: Eugene Lerman
 email: lerman at math uiuc edu
 Homepage:
https://math.uiuc.edu/~lerman
 Course page:
https://math.uiuc.edu/~lerman/519/s16/519s16.html
 Office: 336 Illini Hall
 Office Hours: see my calender and/or
by appointment
 Phone: 2449510
 Class meets: MWF 10 am in 445
Altgeld Hall
 Homework assignments and supplementary notes are posted at
https://math.uiuc.edu/~lerman/519/s16/519s16hw.html
I may also occasionally post my lecture notes on this page
Prerequisites
an introduction to manifolds, differential forms and vector bundles such as math 518.
If you have any questions or concerns, please contact me by email.
Course outline
 review of immersions and embeddings, weakly embedded submanifolds
 Frobenius theorem on the integrability of distributions

review of de Rham cohomology and degree of a proper map, linking numbers.
 principal bundles and associated bundles
 Connections and curvature on principal and vector bundles,
parallel transport
 ChernWeil theory
 (if time permits): Lie groupoids and stacks over manifolds
The following books may be useful:
 Foundations of differentiabler manifolds and Lie groups by Frank W Warner, available through
Springerlink
 Differential Forms in Algebraic Topology by Raoul
Bott and Loring Tu, available through
Springerlink
 Geometry of Differential Forms by Shigyuki Morita
 Deformation Quantization and Index Theory by Boris
Fedosov (first 3035 pages)
 Lectures on SeibergWitten
Invariants by John D. Moore, available through
Springerlink
See this link for homework assignments
and more course related materials
Grades
The
course grade will be based on weekly homework and/or a project
Last modified: Sun Jan 17 13:26:37 CST 2016