Isoperiodic meromorphic forms with at least three simple poles

TL;DR

This paper proves the connectedness of certain moduli spaces of meromorphic differentials with at least three simple poles, leading to new insights into the dynamics of associated foliations.

Contribution

It establishes the connectedness of isoperiodic moduli spaces of meromorphic differentials with three or more simple poles, a novel topological result.

Findings

Connectedness of isoperiodic moduli spaces proven.

Dynamical properties of foliations derived from topological results.

Descriptions of leaf closures in the moduli space provided.

Abstract

In this paper we prove the connectedness of isoperiodic moduli spaces of meromorphic differentials with at least three simple poles on homologically marked smooth curves whose periods are either not contained in a real line, or not contained in the rational space generated by the peripheral periods. From this topological property we deduce dynamical properties of the underlying foliation in the moduli space meromorphic differentials, by describing leaf closures associated to those spaces.