# Dynamics of the absolute period foliation of a stratum of holomorphic 1-forms

@inproceedings{Winsor2021DynamicsOT, title={Dynamics of the absolute period foliation of a stratum of holomorphic 1-forms}, author={Karl Winsor}, year={2021} }

Let Sg be a closed oriented surface of genus g, and let ΩMg(κ) be a stratum of the moduli space of holomorphic 1-forms of genus g. We show that the absolute period foliation of ΩMg(κ) is ergodic on the area-1 locus, and we give an explicit full measure set of dense leaves, subject to a mild constraint on κ. For an algebraically generic cohomology class φ ∈ H(Sg;C), we show that the space of holomorphic 1-forms in ΩMg(κ) representing φ is connected. On the other hand, in the non-generic case, we…

## One Citation

DENSE REAL REL FLOW ORBITS AND ABSOLUTE PERIOD LEAVES

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We show the existence of a dense orbit for real Rel flows on the area-1 locus of every connected component of every stratum of holomorphic 1-forms with at least 2 distinct zeros. For this purpose, we…

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