Oscillations and the Kontsevich-Zorich cocycle

Abstract

We present a mechanism for producing oscillations along the lift of the Teichmüller geodesic flow to the (real) Hodge bundle, as the basepoint surface is deformed by a unipotent element of ${\text{SL}}_2(\mathbb{R})$. Invoking Chen-Möller, we apply our methods to all but finitely many strata in genus $4$, those exhibiting a varying Lyapunov-exponents phenomenon.

12 pages

References in corpus (1)

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