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We compute the sum of the positive Lyapunov exponents of the Hodge bundlewith respect to the Teichmuller geodesic flow. The computation is based on theanalytic Riemann-Roch Theorem and uses a comparison of determinants of flat andhyperbolic Laplacians when the underlying Riemann surface degenerates.

Sum of Lyapunov exponents of the Hodge bundle with respect to the Teichmuller geodesic flow