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Square-tiled surfaces and rigid curves on moduli spaces. (English) Zbl 1227.14030
This paper studies the rigidity of algebraic (Teichmüller) curves arising from square tiled surfaces in the moduli space of curves. It gives a beautiful relation between the limits of slopes for Teichmüller curves and the sums of Lyapunov exponents for the Teichmüller geodesic flow.

##### MSC:
 14H15 Families, moduli of curves (analytic) 32G15 Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) 30F60 Teichmüller theory for Riemann surfaces
##### Keywords:
Branched covers; Lyapunov Exponents; Moduli Space of Curves
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##### References:
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