Document Zbl 1127.58031

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Random spheres and operads. (English) Zbl 1127.58031

J. Geom. Symmetry Phys. 6, 67-84 (2006).

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.

Reviewer: Christian-Oliver Ewald (Leeds)

MSC:

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

Keywords:

stochastic cohomology; loop spaces; Chen-Souriau cohomology

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