Zero Lyapunov exponents and monodromy of the Kontsevich-Zorich cocycle

Abstract

We describe all the situations in which the Kontsevich-Zorich cocycle has zero Lyapunov exponents. Confirming a conjecture of Forni, Matheus, and Zorich, this only occurs when the cocycle satisfies additional geometric constraints. We also describe the real Lie groups which can appear in the monodromy of the Kontsevich-Zorich cocycle. The number of zero exponents is then as small as possible, given its monodromy.

36 pages

References in corpus (2)

• Splitting mixed Hodge structures over affine invariant manifolds
• Square-tiled cyclic covers

Cited by in corpus (9)

• Classification of Rauzy-Veech groups: proof of the Zorich conjecture
• Lower bounds for Lyapunov exponents of flat bundles on curves
• Teichmüller dynamics in the eyes of an algebraic geometer
• The WYSIWYG compactification
• On Selberg's Eigenvalue Conjecture for moduli spaces of abelian differentials
• Lyapunov exponents, holomorphic flat bundles and de Rham moduli space
• Effective Unique Ergodicity and Weak Mixing of Translation Flows
• Quelques contributions à la théorie de l'action de SL(2,R) sur les espaces de modules de surfaces plates
• A Central Limit Theorem for the Kontsevich-Zorich Cocycle