Le cocycle du verger

Abstract

We define and prove uniqueness of a natural homomorphism (called the Orchard morphism) from some groups associated naturally to a finite set $E$ to the group $\mathcal{E}(E)$ of two-partitions of $E$ representing equivalence relations having at most two classes on $E$. As an application, given a finite generic configuration $\mathcal{C}\subset {\mathbf{R}}^d$, we exhibit a natural partition of $\mathcal{C}$ in two sets.

In french, to appear in Comptes rendus de l'Academie des Sciences