A complete stability theorem for foliations with singularities

Abstract

We study codimension one smooth foliations with singularities on closed manifolds. We assume that the singularities are nondegenerate (of Bott–Morse type) in the sense of Scárdua and Seade (2009) [9] and prove a version of Thurston–Reeb stability theorem in terms of a component of the singular set: If all singularities are of center type and the foliation exhibits a compact leaf with trivial Cohomology group of degree one or a codimension ⩾3 component of the singular set with trivial Cohomology group of degree one then the foliation is compact and stable.