Cohomologie de Bismut-Nualart-Pardoux et cohomologie de Hochschild entière

Léandre, Rémi

Séminaire de probabilités de Strasbourg, Tome 30 (1996), pp. 68-99.

[Ar.M] Airault H., Malliavin P. : Quasi sure analysis. Publication Université Paris VI.

[Ar.Mi] Arai A., Mitoma I. : De Rham-Hodge-Kodaira decomposition in infinite dimension. Math. Ann. 291 (1991), 51-73. | MR | Zbl

[At] Atiyah M. : Circular symmetry and stationary phase approximation. pp. 43-59. Colloque en l'honneur de L.Schwartz. Astérisque 131 (1985). | Numdam | MR | Zbl

[B.L] Ben Arous G., Léandre : Décroissance exponentielle du noyau de la chaleur sur la diagonale (II) : P.T.R.F. 90 (1991), 377-402. | MR | Zbl

[B.V] Berline N., Vergne M. : Zéros d'un champ de vecteurs et classes caractéristiques équivariantes. Duke Math. Jour. 50 (1983), 539-548. | MR | Zbl

[Bi1] Bismut J.M. : Large deviations and the Malliavin Calculus. Progress in Math. 45. Birkhaüser. (1984). | MR | Zbl

[Bi2] Bismut J.M. : Index theorem and equivariant cohomology on the loop space. C.M.P. 98 (1985), 213-237. | MR | Zbl

[Bi3] Bismut J.M. : Localisation formulas, superconnections and the index theorem for families. C.M.P. 103 (1986), 127-166. | MR | Zbl

[Ch] Chen K.T. : Iterated path integrals of differential forms and loop space homology. Ann. Math. 97 (1983), 213-237. | MR | Zbl

[Co] Connes A. : Entire cyclic cohomology of Banach algebras and characters of Θ-summable Fredholm modules. K-theory 1 (1988), 519-548. | MR | Zbl

[Dr.R] Driver B., Röckner M. : Construction of diffusion on path and loop spaces of compact riemannian manifold. C.R.A.S. 315. Série I. (1992),603 -608. | MR | Zbl

[El1] Elworthy K.D. : Stochastic differential equations on manifolds. L.M.S. Lectures Notes Serie 20. Cambridge University Press (1982). | MR | Zbl

[El2] Elworthy K.D. : Geometric Aspects of diffusions on manifolds. pp 277-427. In Ecole d'été de Saint-Flour 1987. P.L. Hennequin édit. Lecture Notes in Math. 1362. Springer (1989). | MR | Zbl

[E.L] Emery M., Léandre R. : Sur une formule de Bismut. pp 448-452. Séminaire de Probabilités XXIV. Lecture Notes in Maths. 1426. Springer (1990). | Numdam | MR | Zbl

[F.M] Fang S., Malliavin P. : Stochastic Calculus on Riemannian manifold. Preprint.

[Ge1] Getzler E. : Dirichlet form on a loop space. Bull. Sciences. Math. 2. 113 (1989), 157-174. | MR | Zbl

[Ge2] Getzler E. : Cyclic homology and the path integral of the Dirac operator. Preprint.

[G.J.P] Getzler E., Jones J.D.S. Petrack S. : Differential forms on a loop space and the cyclic bar complex. Topology 30 (1991), 339-373. | MR | Zbl

[Gi] Gilkey P.B. : Invariance theory, the heat-equation and the Atiyah-Singer theorem. Math. Lect. Series. 11. Publish and Perish. | MR | Zbl

[Gr] Gross L. : Potential theory on Hilbert space. J.F.A. 1 (1967), 123-181. | MR | Zbl

[H.K] Hoegh-Krohn R. : Relativistic quantum statistical mechanics in 2 dimensional space time. C.M.P. 38 (1974), 195-224. | MR

[I.W1] Ikeda N., Watanabe S. : Stochastic differential equations and diffusion processes. North-Holland (1981). | MR | Zbl

[J.L1] Jones J., Léandre R. : Lp Chen forms over loop spaces. pp 104-162. In Stochastic Analysis. M.Barlow. N.Bingham edit. Cambridge University Press (1991). | MR | Zbl

[J.L2] Jones J., Léandre R. : A stochastic approach to the Dirac operator over the free loop space. In preparation.

[J.P] Jones J., Petrack S. : The fixed point theorem in equivariant cohomology. Preprint.

[K1] Kusuoka S. : De Rham cohomology of Wiener-Riemannian manifolds. Preprint. | MR

[K2] Kusuoka S. : More recent theory of Malliavin Calculus. Sugaku.5.2. (1992), 155-173. | MR | Zbl

[L1] Léandre R. : Applications quantitatives et qualitatives du calcul de Malliavin. pp 109-133. Proc. Col. Franco-Japonais. M. Métivier. S. Watanabe édit. Lectures Note Math. 1322. Springer. (1988). English translation. pp 173-197. Geometry of Random motion. R. Durrett. M. Pinsky edit. Contemporary Math. 73. (1988). | MR | Zbl

[L2] Léandre R. : Integration by parts formulas and rotationally invariant Sobolev Calculus on free loop spaces. In infinite dimensional problems in physics. XXVIII winter school of theoretical physics. Gielerak R. Borowiec A. edit. Journal of Geometry and Physics. 11 (1993), 517-528. | MR | Zbl

[L3] Léandre R. : Invariant Sobolev Calculus on the free loop space. Preprint. | MR

[L4] Léandre R. : Loop space of a developable orbifold. To be published in the proceedings of the symposium over the brownian sheet. E.Merzbach. J.P.Fouque edts. | Zbl

[L5] Léandre R. : Brownian motion over a Kähler manifold and elliptic genera of level N. To be published in Stochastic analysis and Applications in Physics. L.Streit edt. | MR

[L.R ]Léandre R., Roan S.S. : A stochastic approach to the Euler-Poincaré number of the loop space of a developable orbifold. To be published In Journal of Geometry and Physics. | MR | Zbl

[Nu] Nualart D. : Non causal stochastic integral and calculus. p80-129. In stochastic Analysis. A. Korezlioglu. S. Ustunel edits. Lectures Notes. Math 1316. (1988). | Zbl

[N.P] Nualart D., Pardoux.E. : Stochastics calculus with anticipating integrands. Pro. The. Rela. Fields. 78 (1988), 535-581. | MR | Zbl

[Ra] Ramer R. : On the de Rham complex of finite codimensional forms on infinite dimensional manifolds. Thesis. Warwick University. 1974.

[Sh] Shigekawa I. : De Rham-Hodge-Kodaira's decomposition on an abstract Wiener space. J. Math. Kyoto. Uni. 26 (1986), 191-202. | MR | Zbl

[Sm] Smolyanov O.G. : De Rham currents and Stoke's formula in a Hilbert space. Soviet Math. Dok. 33. 3 (1986), 140-144. | MR | Zbl

[Sm.W] Smolyanov O.G., V.Weizsäcker H. : Differentiable families of measures. Jour. Funct.Ana.118.2. (1993),454-474. | MR | Zbl

[T] Taubes C. : S1 actions and elliptic genera. C.M.P. 122 (1989), 455-526. | MR | Zbl

[Ug] Uglanov Y. : Surface integrals and differential equations on an infinite dimensional space. Sov. Math. Dok. 20.4. (1979), 917-920. | Zbl

[Wa] Watanabe S. : Stochastic analysis and its application. Sugaku.5.1 (1992),51-71. | MR | Zbl