An example of a Teichmuller disk in genus 4 with degenerate Kontsevich-Zorich spectrum

Abstract

We construct an orientable holomorphic quadratic differential on a Riemann surface of genus 4 whose SL(2,R)-orbit is closed and has a highly degenerate Kontsevich - Zorich spectrum. This example is related to a previous similar construction in genus 3 by the first author.

References in corpus (1)

• Connected components of the moduli spaces of Abelian differentials with prescribed singularities

Cited by in corpus (11)

• Sum of Lyapunov exponents of the Hodge bundle with respect to the Teichmuller geodesic flow
• Invariant and stationary measures for the SL(2,R) action on Moduli space
• Symplectic and Isometric SL(2,R) invariant subbundles of the Hodge bundle
• Lyapunov spectrum of invariant subbundles of the Hodge bundle
• Zero Lyapunov exponents of the Hodge bundle
• Non-varying sums of Lyapunov exponents of Abelian differentials in low genus
• Invariant Subvarieties of Minimal Homological Dimension, Zero Lyapunov Exponents, and Monodromy
• Some examples of isotropic SL(2,R)-invariant subbundles of the Hodge bundle
• Statistics of Square-tiled Surfaces: Symmetry and Short Loops
• The Extrinsic Primitive Torsion Problem
• Oscillations and the Kontsevich-Zorich cocycle