Affine Manifolds and Zero Lyapunov Exponents in Genus 3
Dynamical Systems
2015-12-22 v2 Geometric Topology
Abstract
In previous work, the author fully classified orbit closures in genus three with maximally many (four) zero Lyapunov exponents of the Kontsevich-Zorich cocycle. In this paper, we prove that there are no higher dimensional orbit closures in genus three with any zero Lyapunov exponents. Furthermore, if a Teichm\"uller curve in genus three has two zero Lyapunov exponents in the Kontsevich-Zorich cocycle, then it lies in the principal stratum and has at most quadratic trace field. Moreover, there can be at most finitely many such Teichm\"uller curves.
Keywords
Cite
@article{arxiv.1409.5180,
title = {Affine Manifolds and Zero Lyapunov Exponents in Genus 3},
author = {David Aulicino},
journal= {arXiv preprint arXiv:1409.5180},
year = {2015}
}
Comments
40 pages, To appear in GAFA