Stability of foliations of 3-manifolds by circles (Q1085844)

Let M be a closed 3-manifold and let \({\mathcal F}\) be a foliation of M by circles; the necessary and sufficient conditions for \({\mathcal F}\) to be stable are given. These are: (1) \(\chi\) (M/\({\mathcal F})^ 2+\chi_ V(M/{\mathcal F})^ 2\neq 0\), where \(\chi_ V(M/{\mathcal F})\) is the V-Euler characteristic of the leaf space M/\({\mathcal F}\) [\textit{I. Satake}, ibid. 9, 464-492 (1957; Zbl 0080.374)]. (2) The union of all reflection leaves of \({\mathcal F}\) contains a subset homeomorphic to a Klein bottle.