Sufficient conditions for the compactifiability of a closed one-form foliation

Authors: IRINA GELBUKH

Abstract: We study the foliation defined by a closed $1$-form on a connected smooth closed orientable manifold.We call such a foliation compactifiable if all its leaves are closed in the complement of the singular set.In this paper, we give sufficient conditions for compactifiability of the foliation in homological terms.We also show that under these conditions, the foliation can be defined by closed $1$-forms with the ranks of their groups of periods in a certain range.In addition, we describe the structure of the group generated by the homology classes of all compact leaves of the foliation.

Keywords: Closed one-form foliation, compact leaves, form's rank,

Full Text: PDF