**E. Ballico**

## The Non-Vanishing of First Cohomology Groups for
Certain Infinite-Dimensional Complex Manifolds

**Abstract:**

Here, using the ideas of an old paper by S. Dineen (1976), 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.

**Keywords:**

Infinite-dimensional complex manifold, first Cousin problem, additive Cousin
problem, non-vanishing of cohomology.

**MSC 2000:** 32L05, 32K05