Surfaces transverse to pseudo-Anosov flows and virtual fibers in 3-manifolds (Q1292706)

Let \(S\) be a surface immersed in a closed 3-manifold \(M\) so that \(S\) is transverse to a pseudo-Anosov flow \(\Phi\) on \(M\). The flow \(\Phi\) induces stable and unstable foliations in \(S\). The main result of the present paper is that \(S\) is a virtual fibre if and only if the induced foliations do not have closed leaves. \(S\) is called a virtual fibre, if \(M\) fibers over the circle and there is a finite cover of \(M\) such that \(S\) lifts to a surface which is homotopic to a fibre in this cover. The proof uses a careful study of the behaviour of the lifts of \(S\) to the universal cover and the relations of the lifts to the singular stable and unstable foliations.