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Zbl 0870.58011
Léandre, R.
Bismut-Nualart-Pardoux cohomology and entire Hochschild cohomology. (Cohomologie de Bismut-Nualart-Pardoux et cohomologie de Hochschild entière.) (French)
[A] Azéma, J. (ed.) et al., Séminaire de probabilités XXX. Berlin: Springer. Lect. Notes Math. 1626, 68-99 (1996). ISBN 3-540-61336-6/pbk

Let $M$ be a compact, finite-dimensional, Riemannian manifold, $P(M)$ the space of paths and $L(M)$ the space of free loops on $M$.\par The article consists of two parts. The first part, using a regularity defined by {\it D. Nualart} and {\it E. Pardoux} [Probab. Theory Relat. Fields 78, No. 4, 535-581 (1988; Zbl 0629.60061)], is building a version of stochastic exterior derivative on the space of $C^\infty$-forms in Nualart-Pardoux sense. This stochastic exterior derivative leads to $H^\infty(P)$, the entire Nualart-Pardoux cohomology, $H^p(P)$, the Bismut-Nualart-Pardoux cohomology of order $p$, and $H^\infty$(flat). It is proved that $H^\infty (\text {flat}) =H(M)$.\par In the second part, following {\it E. Getzler}, {\it J. Jones} and {\it S. Petrack} [Topology 30, No. 3, 339-371 (1991; Zbl 0729.58004)] a commutative diagram of complexes is used to prove the equality between the entire Hochschild cohomology and the stochastic cohomology on the loop space.
[M.Crasmareanu (Iaşi)]

MSC 2000:: *58D15 Manifolds of mappings
55N20 Generalized homology and cohomology theories
60H05 Stochastic integrals
58J10 Differential complexes
58A10 Differential forms

Keywords: $C\sp \infty$-forms in Nualart-Pardoux sense; stochastic exterior derivative; entire Hochschild cohomology; stochastic cohomology; loop space

Citations: Zbl 0629.60061; Zbl 0729.58004

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