Quadratic differentials with prescribed singularities and pseudo-Anosov diffeomorphisms (Q1311210)

In this paper the authors determine which collections of ``topological'' data on a Riemannian surface \(M\) can be realized by quadratic differentials with finite area on \(M\). As a corollary they determine which topological data can be realized by pseudo-Anosov diffeomorphisms on oriented surfaces. The topological data in question are the genus of \(M\); the orders of zeros and poles of the quadratic differential and the orientability of its horizontal foliation; the types of singularities and the orientability of the stable foliation of the pseudo-Anosov diffeomorphism.