The topology of foliations formed by the generic K-orbits of a subclass of the indecomposable MD5-groups

The paper is a continuation of the authors’ works in 2007. We consider the MD5-foliations associated to connected and simply connected MD5-groups such that their Lie algebras have 4-dimensional commutative derived ideals. In this study, we give a topological classification of all considered MD5-foliations. A description of these foliations by certain fibrations or suitable actions of R2 and the Connes’ C*-algebras of the foliations which come from fibrations are also given.