Complex homogeneous spaces of real groups with top homology in codimension two (Q1897597)

Let \(G/H\) be a connected complex manifold, \(G\) being a Lie group and \(H\) a closed subgroup. Assume \({\mathcal O}(x)\neq\mathbb{C}\) and let \(G/H\to G/I\) be the holomorphic reduction of \(X\). It is shown that if the top nonvanishing homology group of \(X\) with coefficients in \(\mathbb{Z}_2\) is of codimension two, then either a complex Lie group acts transitively on \(G/I\) or \(G/I\) is biholomorphic to the unit disc.