Random Spheres and Operads

Abstract

We define a stochastic diffeology over the n-fold loop-space of a n-connected manifold. We perform a stochastic cohomology in the sense of Chen and Souriau and we show that the stochastic cohomology groups are equal to the classical de Rham cohomology groups of the n-fold loop space. We give a stochastic analogue of the classical fact that the homology groups of the n-fold loop space are an algebra for the little cube operad.