Bundles and Characteristic Classes

Course Information:

Math 542: Bundles and Characteristic Classes

Official Course Description:

The main goal of this course is to discover various cohomology classes (i.e. "characteristic classes") of a (smooth) manifold encoded in its tangent bundle (and other associated bundles).

This course will cover the following topics:

• Summary of smooth manifolds and tangent spaces
• Vector (and fiber) bundles, building toward characteristic classes
  • Stiefel--Whitney class
  • Euler class
  • Chern class
  • Pontryagin class
• Existence of exotic smooth structures on S⁷ (time permitting)

Texts:

1. John Milnor & James D. Stasheff. (1974) Characteristic classes.

Professor Neil FULLARTON

Office: HBH 420

Website: http://math.rice.edu/~nf8/

Lecture

Course Announcements:

• (12 Jan 2016) The Bundles and Characteristic Classes course page is now online.