Basic Information

• Instructor: Eugene Lerman
• e-mail: lerman at math uiuc edu
• Homepage: http://www.math.uiuc.edu/~lerman
• Course page: http://www.math.uiuc.edu/~lerman/519/s16/519s16.html
• Office: 336 Illini Hall
• Office Hours: see my calender and/or by appointment
• Phone: 244-9510
• Class meets: MWF 10 am    in 445 Altgeld Hall
• Homework assignments and supplementary notes are posted at
  http://www.math.uiuc.edu/~lerman/519/s16/519s16hw.html
  I may also occasionally post my lecture notes on this page

Prerequisites

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
  
• Chern-Weil 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 30-35 pages)
• Lectures on Seiberg-Witten Invariants by John D. Moore, available through Springerlink

See this link for homework assignments and more course related materials

Grades