Language:   Search:   Contact
Zentralblatt MATH has released its new interface!
For an improved author identification, see the new author database of ZBMATH.

Query:
Fill in the form and click »Search«...
Format:
Display: entries per page entries
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

Highlights
Master Server

### Zentralblatt MATH Berlin [Germany]

© FIZ Karlsruhe GmbH

Zentralblatt MATH master server is maintained by the Editorial Office in Berlin, Section Mathematics and Computer Science of FIZ Karlsruhe and is updated daily.

Other Mirror Sites

Copyright © 2013 Zentralblatt MATH | European Mathematical Society | FIZ Karlsruhe | Heidelberg Academy of Sciences