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Stochastic algebraic de Rham complexes. (English) Zbl 1039.58031
In this very interesting paper the author continues his study of extension of the de Rham complexes for finite dimensional compact manifolds $M$ to the infinite dimensional manifolds -- the loop spaces associated to such manifolds. The work is an interplay between the topological properties of such manifolds and the stochastic properties associated with Brownian motion on such manifolds and their infinite dimensional loop spaces. The work addresses the issue of correct extension of the de Rham cohomology known for finite dimensional manifolds to the associated infinite dimensional manifolds using methods of stochastic analysis based on Malliavin calculus. Partial success in resolving this issue constitutes the essence of this work

##### MSC:
 58J65 Diffusion processes and stochastic analysis on manifolds 57R55 Differentiable structures 60H07 Stochastic calculus of variations and the Malliavin calculus
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