Codimension two compact Hausdorff foliations by hyperbolic surfaces are not stable (Q1840910)

A foliation \({\mathcal F}\) is said to be stable if any small perturbation of \({\mathcal F}\) has a compact leaf; when not, \({\mathcal F}\) is called unstable. The main result of the paper is that all compact Hausdorff \({\mathcal C}^r\)-foliations, \(1\leq r \leq \infty\), by hyperbolic surfaces (i.e. closed orientable surfaces of genus \(\geq 2\)) on any \(4\)-dimensional \({\mathcal C}^r\)-manifold (compact or not) are \({\mathcal C}^r\)-unstable.