Hill, C. Denson; Nacinovich, M. Duality and distribution cohomology of CR manifolds. (English) Zbl 0848.32003 Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 22, No. 2, 315-339 (1995). From authors’ summary: “Our aim here is to investigate the \(\overline \partial_M\)-complexes on currents in the sense of G. de Rham [‘Variétés différentiables’, Hermann, Paris (1960; Zbl 0089.08105)], associated to a CR manifold \(M\) of arbitrary dimension and codimension. This brings into play global distribution \(\overline \partial_M\)-cohomology on \(M\), and involves its relationship to the smooth \(\overline \partial_M\)-cohomology on \(M\), as well as its connection with the classical Dolbeault cohomology of an ambient complex manifold \(X\), in the case where \(M\) is assumed to be embeddable. We also discuss compact abstract CR manifolds \(M\), and achieve a duality formula which is in the spirit of de Rham and J.-P. Serre [Comment Math. Helv. 29, 9-26 (1955; Zbl 0067.16101)] for real and complex manifolds respectively, and which is related to the work by A. Andreotti and A. Kas [Ann. Sc. Norm. Super. Pisa, Sci. fis. mat., III. Ser. 27, 187-263 (1973; Zbl 0278.32007)] and A. Andreotti and C. Banica [Rev. Roum. Math. Pure Appl. 20, 981-1041 (1975; Zbl 0305.58001)]. Reviewer: N.Mihalache (Bucureşti) Cited in 1 ReviewCited in 8 Documents MSC: 32V99 CR manifolds 32F10 \(q\)-convexity, \(q\)-concavity Keywords:\(\overline \partial_ M\)-complex; distribution cohomology; CR manifolds; duality Citations:Zbl 0089.08105; Zbl 0067.16101; Zbl 0278.32007; Zbl 0305.58001 PDFBibTeX XMLCite \textit{C. D. Hill} and \textit{M. Nacinovich}, Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 22, No. 2, 315--339 (1995; Zbl 0848.32003) Full Text: Numdam EuDML References: [1] R.A. Ajrapetyan - G.M. Henkin , Integral representations of differential forms on Cauchy-Riemann manifolds and the theory of CR functions I, II , Usp. Mat. 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