PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Mary Anne Raymond.

Title:Foliations and their characteristic classes
Seminar:Slow Pitch Seminar
Speaker:Dmitry Fuchs, UC Davis
Abstract:
A k-dimensional foliation on a manifold M is as an integrable field of k-dimensional subspaces of tangent spaces of M (where k < dim M). Integrability means that every point of M belongs to a k-dimensional submanifold of M everywhere tangent to the planes of the field. These manifolds, called leaves, locally look like families of parallel k-planes; however, globally their behaviour is less decent. (Examples will be shown.) In the 70-s, characteristic classes of foliations were discovered; the simplest of them, the so called Godbillon-Vey class, is a 3-dimensional cohomology class of a manifold with a codimension 1 (dimension dim M -1) foliation. Although the definition of this class is extremely simple, its geometric meaning remains very much unclear. There are exciting unsolved problems which are very easy to formulate but, apparently, not so easy to solve. The talk will be elementary. The most advanced notion used will be that of a diffrential form.

Room Reservation Information

Room Number:MB106
Date:02 / 19 / 2008
Time:05:15pm - 06:15pm