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

TL;DR

This paper classifies the topology of foliations formed by generic K-orbits of specific MD5-groups with 4-dimensional commutative derived ideals, describing their structure via fibrations and analyzing associated C*-algebras.

Contribution

It provides a topological classification of MD5-foliations for a subclass of MD5-groups and describes their structure through fibrations and group actions, extending previous work.

Findings

Topological classification of all considered MD5-foliations

Descriptions of foliations via fibrations and group actions

Analysis of Connes' C*-algebras associated with these foliations

Abstract

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.