Periods of abelian differentials and dynamics

TL;DR

This paper characterizes cohomology classes that serve as period characters of abelian differentials on surfaces, using Ratner's theorem to connect complex structures with dynamical systems.

Contribution

It provides a classification of period characters of abelian differentials on surfaces, linking complex geometry with homogeneous dynamics.

Findings

Characterization of cohomology classes as period characters

Application of Ratner's theorem to complex structures

Connection between geometry and dynamics in surface theory

Abstract

Given a closed oriented surface S we describe those cohomology classes which appear as the period characters of abelian differentials for some choice of complex structure on S consistent with the orientation. The proof is based upon Ratner's solution of Raghunathan's conjecture.