Random spheres and operads. (English) Zbl 1127.58031

The author constructs a stochastic Chen-Souriau diffeological calculus of the \(n\)-fold loop space of an \(n\)-connected compact manifold and shows that the stochastic cohomology of the stochastic \(n\)-fold loops pace is equal to the (deterministic) cohomology of the Hölder \(n\)-fold loop space. Furthermore the author defines an action of the little cube operad on the stochastic \(n\)-fold loop space and deduces that the stochastic homology groups of the \(n\)-fold loop space are an algebra with respect to this operad.


58J65 Diffusion processes and stochastic analysis on manifolds
58D15 Manifolds of mappings
60H40 White noise theory