## 1. NRW Topology Meeting -- Bonn (Germany)

### 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