• E.mail: groves@caltech.edu
• Office: 176 Sloan Office Phone: 4322
• Office Hours:
  • TBA
Web page: www.its.caltech.edu/~groves/151c2007/
• Homework Assignments

Course Description: 

Math 151 is the year-long graduate sequence in topology and geometry. In the third term, we will concentrate on characteristic classes, mostly following Milnor and Stasheff. We will start with a brief introduction to spectral sequences, then discuss smooth manifolds and vector bundles. Then we will spend most of the quarter discussing characteristic classes. We will not cover all of Milnor and Stasheff. Characteristic classes are useful invariants of vector bundles. Example of vector bundles include the tangent space of a manifold, and one use of characteristic classes is in higher dimensional analogues of the Gauss-Bonnet formula, linking curvature properties to topological properties or combinatorial properties of the manifold. Another application is the construction of exotic smooth structures on the 7-sphere.

Prerequisite: Ma151b

Text:Characteristic Classes, Milnor and Stasheff

Homework Assignments:

All problem numbers refer to Milnor and Stasheff, except as noted.