The Topology of Foliations Formed by the Generic K-Orbits of a Subclass of the Indecomposable MD5-Groups

The present paper is a continuation of [13], [14] of the authors. Specifically, the paper considers the MD5-foliations associated to connected and simply connected MD5-groups such that their Lie algebras have 4-dimensional commutative derived ideal. In the paper, we give the topological classification of all considered MD5-foliations. A description of these foliations by certain fibrations or suitable actions of $\mathbb{R}^{2}$ and the Connes' C*-algebras of the foliations which come from fibrations are also given in the paper.