Ballico, E. The non-vanishing of first cohomology groups for certain infinite-dimensional complex manifolds. (English) Zbl 1065.32011 Georgian Math. J. 12, No. 1, 11-13 (2005). Summary: Here, using the ideas of an old paper by S. Dineen [An. Acad. Brasil. Ci. 48, No. 1, 11–12 (1976; Zbl 0354.46029)], we give large classes of pairs \((X, E)\) such that \(X\) is an infinite-dimensional complex space very far from a Banach manifold, \(E\) is a holomorphic vector bundle on \(X\) and \(H^1(X, E)\) is infinite-dimensional. MSC: 32L05 Holomorphic bundles and generalizations 32K05 Banach analytic manifolds and spaces 46G99 Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces) Keywords:infinite-dimensional complex manifold; first Cousin problem; additive Cousin problem; non-vanishing of cohomology Citations:Zbl 0354.46029 PDFBibTeX XMLCite \textit{E. Ballico}, Georgian Math. J. 12, No. 1, 11--13 (2005; Zbl 1065.32011)