COCATÉGORIE ET NILPOTENCE

Abstract

The Lusternik-Schnirelmann category of a topological space X, denoted catX, is the least integer n such that X can be covered by n + 1 open sets, each of them contractible in X.  This is a homotopical invariant.  We give dualisation of this invariant in the sense of Eckmann-Hilton and we show that the nilpotent class of the space [G,X] is a lower bound.