A large deviations bound for the Teichmuller flow

Large deviation rates are obtained for suspension flows over symbolic dynamical systems with a countable alphabet. The method is that of the first author and follows that of L.-S. Young. A corollary of the main results is a large deviation bound for the Teichm"uller flow on the moduli space of abelian differentials, which extends earlier work of J. Athreya.