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Zbl 1037.58025
Léandre, Rémi
Stochastic Adams theorem for a general compact manifold. (English)
[J] Rev. Math. Phys. 13, No. 9, 1095-1133 (2001). ISSN 0129-055X

Let $M$ be a compact Riemannian simply connected manifold, and let $L_x(M)$ be the loop space based at $x\in M$, endowed with the Brownian bridge law and with $H$-derivation.\par The main result here is that over $L_x(M)$ the stochastic cohomology of smooth forms equals the Hochschild cohomology. This is the stochastic analysis counterpart of the analogous theorem by Adams, which concerns smooth loops.\par The main step in the long proof of this result is to identify the cohomologies of smooth forms over $L_x(M)$ and over the space of paths on $M$ which start from $x$ and arrive in some open neighborhood of $x$.
[Jacques Franchi (Strasbourg)]

MSC 2000:: *58J65 Diffusion processes and stochastic analysis on manifolds
60H07 Stochastic calculus of variations and the Malliavin calculus
60J65 Brownian motion

Keywords: loop space; Brownian bridge law; smooth forms; Hochschild cohomology

Cited in: Zbl 1059.81111

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