Lyapunov spectrum of invariant subbundles of the Hodge bundle

Abstract

We study the Lyapunov spectrum of the Kontsevich--Zorich cocycle on $SL(2,\mathbb{R})$-invariant subbundles of the Hodge bundle over the support of a $SL(2,\mathbb{R})$-invariant probability measure on the moduli space of Abelian differentials. In particular, we prove formulas for partial sums of Lyapunov exponents in terms of the second fundamental form (or Kodaira--Spencer map) of the Hodge bundle with respect to Gauss--Manin connection and investigate the relations between the central {Oseldets} subbundle and the kernel of the second fundamental form. We illustrate our conclusions in two special cases.

67 pages, 2 figures. New version based on the reports of the referees. To appear in ETDS

References in corpus (4)

• Sum of Lyapunov exponents of the Hodge bundle with respect to the Teichmuller geodesic flow
• An example of a Teichmuller disk in genus 4 with degenerate Kontsevich-Zorich spectrum
• Square-tiled cyclic covers
• Lyapunov spectrum of ball quotients with applications to commensurability questions

Cited by in corpus (8)

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• Full rank affine invariant submanifolds
• Lyapunov spectrum of ball quotients with applications to commensurability questions
• Eigenvalues of Curvature, Lyapunov exponents and Harder-Narasimhan filtrations
• Limits of geodesic push-forwards of horocycle invariant measures
• Counting problem on wind-tree models
• On ergodicity of foliations on ${\mathbb{Z}}^d$-covers of half-translation surfaces and some applications to periodic systems of Eaton lenses
• Affine Manifolds and Zero Lyapunov Exponents in Genus 3