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The non-vanishing of first cohomology groups for certain infinite-dimensional complex manifolds. (English) Zbl 1065.32011

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)

Citations:

Zbl 0354.46029
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