  Consider the 1-dimensional Hurwitz space parameterizing covers of P^1
branched at four points. We study its intersection with divisor classes on the
moduli space of curves. As an application, we calculate the slope of the
Teichmuller curve parameterizing square-tiled cyclic covers and recover the sum
of its Lyapunov exponents obtained by Forni, Matheus and Zorich. Motivated by
the work of Eskin, Kontsevich and Zorich, we exhibit a relation among the slope
of Hurwitz spaces, the sum of Lyapunov exponents and the Siegel-Veech constant
for the moduli space of quadratic differentials.

Algebraic Geometry;Dynamical Systems;Geometric Topology