De Rham-Hodge-Kodaira decomposition in \(\infty\)-dimensions

DOI10.1007/BF01445190zbMath0762.58004OpenAlexW2314353375MaRDI QIDQ1191420

Asao Arai, Itaru Mitoma

Publication date: 27 September 1992

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/164849

zbMATH Keywords

de Rham complexinfinite dimensional analysisspaces of test functionalsde Rham-Hodge-Kodaira decompositionsspaces of differential 0- forms

Mathematics Subject Classification ID

de Rham theory in global analysis (58A12) Stochastic analysis (60H99) Homotopy and topological questions for infinite-dimensional manifolds (58B05)

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COVER OF THE BROWNIAN BRIDGE AND STOCHASTIC SYMPLECTIC ACTION ⋮ A stochastic approach to the Euler-Poincaré number of the loop space of a developable orbifold ⋮ \(L^{2}\)-Betti numbers of infinite configuration spaces ⋮ Fedosov Quantization in White Noise Analysis ⋮ Laplace operators in deRham complexes associated with measures on configuration spaces ⋮ An \(L^{2}\) theory for differential forms on path spaces. I ⋮ Dirac operators in Boson-Fermion Fock spaces and supersymmetric quantum field theory ⋮ Fermionic and supersymmetric stochastic processes ⋮ Laplace operators on differential forms over configuration spaces ⋮ Transformations on white noise functions associated with second order differential operators of diagonal type ⋮ A sheaf-theoretical approach to stochastic cohomology ⋮ De Rham cohomology of configuration spaces with Poisson measure ⋮ A STOCHASTIC APPROACH TO THE EULER–POINCARE CHARACTERISTIC OF A QUOTIENT OF A LOOP GROUP ⋮ Commutation properties of anticommuting self-adjoint operators, spin representation and Dirac operators ⋮ Strong anticommutativity of dirac operators on boson—fermion fock spaces and representations of a supersymmetry algebra ⋮ Differentiable measures and the Malliavin calculus ⋮ Stochastic equivariant cohomologies and cyclic cohomology ⋮ The heat kernel weighted Hodge Laplacian on noncompact manifolds ⋮ Stochastic analysis on product manifolds: Dirichlet operators on differential forms

Cites Work

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• Lectures on stochastic differential equations and Malliavin calculus
• Sobolev spaces of Wiener functionals and Malliavin's calculus
• De Rham-Hodge-Kodaira's decomposition on an abstract Wiener space
• Index of a family of Dirac operators on loop space
• On dimensional reduction of functional measures
• Dirichlet forms and white noise analysis
• A general class of infinite dimensional Dirac operators and path integral representation of their index
• Applications of a commutation formula
• Path integral representation of the index of Kähler-Dirac operators on an infinite dimensional manifold
• The Heat Equation for Riemannian Foliations
• On Meyer’s equivalence
• A Segal-Langevin Type Stochastic Differential Equation on a Space Of Generalized Functionals

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