Lyapunov spectrum of square-tiled cyclic covers

Abstract

A cyclic cover over $CP^1$ branched at four points inherits a natural flatstructure from the 'pillow' flat structure on the basic sphere. We give anexplicit formula for all individual Lyapunov exponents of the Hodge bundle overthe corresponding arithmetic Teichmüller curve. The key technical element isevaluation of degrees of line subbundles of the Hodge bundle, corresponding toeigenspaces of the induced action of deck transformations.