Nonvarying sums of Lyapunov exponents of Abelian differentials in low genus

摘要

We show that for many strata of Abelian differentials in low genus the sum of Lyapunov exponents for the Teichmuller geodesic flow is the same for all Teichmuller curves in that stratum, hence equal to the sum of Lyapunov exponents for the whole stratum. This behavior is due to the disjointness property of Teichmuller curves with various geometrically defined divisors on moduli spaces of curves.