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Quadratic differentials with prescribed singularities and pseudo-Anosov diffeomorphisms. (English) Zbl 0792.30030
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.

30F30 Differentials on Riemann surfaces
37Cxx Smooth dynamical systems: general theory
Full Text: DOI EuDML