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

Alex Eskin; Anton Zorich; Maxim Kontsevich

arxiv: 1112.5872 · v6 · pith:6TOGBMILnew · submitted 2011-12-26 · 🧮 math.DS · math.AG· math.GT

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

Alex Eskin , Maxim Kontsevich , Anton Zorich This is my paper

classification 🧮 math.DS math.AGmath.GT

keywords bundleexponentsflowgeodesichodgelyapunovrespectteichmuller

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

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

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