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

Abstract

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.

Minor corrections. To appear in Publications mathematiques de l'IHES

References in corpus (8)

• Geometry of the Weil-Petersson completion of Teichmüller space
• An example of a Teichmuller disk in genus 4 with degenerate Kontsevich-Zorich spectrum
• Square-tiled cyclic covers
• Right-angled billiards and volumes of moduli spaces of quadratic differentials on $\mathbb{C}{P}^1$
• Compact polyhedral surfaces of an arbitrary genus and determinants of Laplacians
• Zero Lyapunov exponents of the Hodge bundle
• Covers of the projective line and the moduli space of quadratic differentials
• Non-varying sums of Lyapunov exponents of Abelian differentials in low genus

Cited by in corpus (53)

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• Zero Lyapunov exponents and monodromy of the Kontsevich-Zorich cocycle
• Lyapunov spectrum of invariant subbundles of the Hodge bundle
• Masur-Veech volumes, frequencies of simple closed geodesics and intersection numbers of moduli spaces of curves
• Topological recursion for Masur-Veech volumes
• Large Genus Asymptotics for Intersection Numbers and Principal Strata Volumes of Quadratic Differentials
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• Masur-Veech volumes and intersection theory: the principal strata of quadratic differentials
• Cohomology classes of strata of differentials
• Lower bounds for Lyapunov exponents of flat bundles on curves
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• Affine geometry of strata of differentials
• Square-tiled surfaces and rigid curves on moduli spaces
• Eigenvalues of Curvature, Lyapunov exponents and Harder-Narasimhan filtrations
• Quasimodularity and large genus limits of Siegel-Veech constants
• Degenerations of Abelian Differentials
• Teichmüller dynamics in the eyes of an algebraic geometer
• Square-tiled surfaces of fixed combinatorial type: equidistribution, counting, volumes of the ambient strata
• Zero Lyapunov exponents of the Hodge bundle
• Covers of the projective line and the moduli space of quadratic differentials
• Quadratic differentials in low genus: exceptional and non-varying
• Non-varying sums of Lyapunov exponents of Abelian differentials in low genus
• Counting problem on wind-tree models
• Loci in strata of meromorphic differentials with fully degenerate Lyapunov spectrum
• Geometry of periodic regions on flat surfaces and associated Siegel-Veech constants
• Measure bound for translation surfaces with short saddle connections
• A non-varying phenomenon with an application to the wind-tree model
• SL(2,R)-invariant probability measures on the moduli spaces of translation surfaces are regular
• Volumes of the sets of translation surfaces with small saddle connections in rank one affine submanifolds
• Affine Manifolds and Zero Lyapunov Exponents in Genus 3
• Strata of abelian differentials and the Teichmueller dynamics
• Counting generalized Jenkins-Strebel differentials
• On the number of saddle connections in translation surfaces with poles
• Euler characteristics of Gothic Teichmüller curves
• Moduli space of meromorphic differentials with marked horizontal separatrices
• Invariant Subvarieties of Minimal Homological Dimension, Zero Lyapunov Exponents, and Monodromy
• Schwarz triangle mappings and Teichmüller curves: the Veech-Ward-Bouw-Möller curves
• Masur--Veech volumes of quadratic differentials and their asymptotics
• Lyapunov exponents, holomorphic flat bundles and de Rham moduli space
• Counting special Lagrangian fibrations in twistor families of K3 surfaces
• Quantitative error term in the counting problem on Veech wind-tree models
• Parabolic Higgs bundles, $t{t}^{\ast }$ connections and opers
• Billiards in right triangles and orbit closures in genus zero strata
• Tautological ring of strata of differentials
• A coding-free simplicity criterion for the Lyapunov exponents of Teichmueller curves
• Quelques contributions à la théorie de l'action de SL(2,R) sur les espaces de modules de surfaces plates
• What are Lyapunov exponents, and why are they interesting?
• Singular Fibers and Kodaira Dimensions
• Pillowcase covers: Counting Feynman-like graphs associated with quadratic differentials
• Relative systoles in hyperelliptic translation surfaces