### Mathematisches Kolloquium

### Friday, April 23, 2004

### 17.15 - 18.15, Kleiner Hörsaal, Wegelerstr. 10

### Prof. Elmar Vogt (FU Berlin):
Lusternik-Shnirelmann category for spaces and foliations

Abstract:
The Lusternik-Shnirelmann category of a space X is the smallest number k
such that X can be covered by (k+1) open sets which are contractible in X.
This number, denoted by catX, is of interest since it is a lower bound for
the number of critical points for any smooth function on X if X is a
manifold, since it is a homotopy invariant, and since it is hard to
compute and therefore a challenge.
After explaining some of the results known about catX, I will describe a
generalization of catX to foliations and investigate which results of catX
survive in the new context. A foliation of an n-manifold M is a
decomposition of M into p-dimensional immersed submanifols which looks
locally like the decomposition of R^n into R^p\times R^(n-p).
Equivalently it is the decomposition of M into the maximal solutions of a
completely integrable system of forms of rank n-p.

06.04.04 -- Stefan Schwede