On the complex analytic Gel'fand-Fuks cohomology of open Riemann surfaces

Nariya Kawazumi

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Jerry M. Lodder (1998)

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We propose a definition of Leibniz cohomology, $H L^{*}$ , for differentiable manifolds. Then $H L^{*}$ becomes a non-commutative version of Gelfand-Fuks cohomology. The calculations of $H L^{*} (R^{n}; R)$ reduce to those of formal vector fields, and can be identified with certain invariants of foliations.

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Marius Van der Put (1990)

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Olaf Ermert (1999)

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We compute the algebraic and continuous Hochschild cohomology groups of certain Fréchet algebras of analytic functions on a domain U in $ℂ^{n}$ with coefficients in one-dimensional bimodules. Among the algebras considered, we focus on A=A(U). For this algebra, our results apply if U is smoothly bounded and strictly pseudoconvex, or if U is a product domain.

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Hyperfunction cohomology classes and their boundary values

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