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 |