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Consider a foliation of a compact manifold with all leaves compact. When must any \(C^ 0\)-perturbation of this foliation have a compact leaf? \textit{R. Langevin} and \textit{H. Rosenberg} [Lect. Notes Math. 652, 122-127 (1978; Zbl 0382.57011)] proved that any such perturbation of a fibration over a surface with nonzero Euler characteristic has a compact leaf if the fundamental group of the fiber is \({\mathbb{Z}}\) and the fundamental group of the base acts trivially on the fundamental group of the fiber. The present author generalizes this result to codimension-two foliations with the ''base'' being the leaf space of the foliation and an additional assumption of no ''isolated singular leaf''.
perturbations of foliations, codimension-two foliations, generalized Seifert fibre space, 57R30, Foliations in differential topology; geometric theory, Stability theory for smooth dynamical systems, stability of compact leaves, foliation of a compact manifold with all leaves compact
perturbations of foliations, codimension-two foliations, generalized Seifert fibre space, 57R30, Foliations in differential topology; geometric theory, Stability theory for smooth dynamical systems, stability of compact leaves, foliation of a compact manifold with all leaves compact
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