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

Masur, Howard; Smillie, John

Comment. Math. Helv. 68, No. 2, 289-307 (1993).

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.

Reviewer: V.L.Hansen (Lyngby)

MSC:

30F30	Differentials on Riemann surfaces
37Cxx	Smooth dynamical systems: general theory

Keywords:

quadratic differentials; pseudo-Anosov diffeomorphisms