Godbillon-Vey classes of Lie subalgebroids

Abstract

The Godbillon-Vey class is a secondary characteristic class which is defined for regular foliations and have been studied extensively. On the other hand, extending the Godbillon-Vey class to singular foliations is difficult, and a complete result has not yet been obtained. In this paper, we address this problem by focusing on a geometric object called a Lie algebroid on a manifold. More precisely, we fix a Lie algebroid and relatively define the Godbillon-Vey class for its Lie subalgebroids, and study their properties. We also present several examples.