Stability of a compact leaf homeomorphic to the Klein bottle and its applications (Q921666)

The space of \(C^{\infty}\)-foliations of codimension q has a \(C^ r\)- topology. A codimension q foliation is said to be \(C^ r\)-stable if every nearby foliation in this topology has a compact leaf. In a previous paper [Publ. Res. Inst. Math. Sci. 22, 1155-1171 (1986; Zbl 0623.57017)] the author studied the stability of the foliations of 4-manifolds by orientable surfaces. In the present paper, he studies the same problem for the foliations of 4-manifolds with non-orientable closed surfaces and obtains some sufficient conditions for such foliations to be stable.