Isoperiodic meromorphic forms: two simple poles

Abstract

In this paper, we prove that isoperiodic moduli spaces of meromorphic differentials with two simple poles on homologically marked smooth curves are non-empty and connected unless they correspond to double covers of $\mathbb{C}/\mathbb{Z}$ on curves of genus at least two. We deduce dynamical consequences for the corresponding isoperiodic foliation.