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October 2, 2025Open Access

Topology of singular foliations of closed 1-forms on orbifolds

Key Points

All leaves can be either compact or non-compact based on a closed 1-form's properties.
Criteria established help to characterize the topology of such leaves on orbifolds.
The work generalizes Calabi's result on harmonic 1-forms, providing new insights on orbifolds.
Understanding the coexistence of compact and non-compact leaves can impact further research in topology.

Abstract

We study the topological properties of the leaves of the singular foliation induced by a closed 1-form of Morse type on a compact orbifold. In particular, we establish criteria that characterize when all such leaves are compact, when they are non-compact, and how both types may coexist. As an application, we extend to the orbifold setting a celebrated result of Calabi, which provides a purely topological characterization of intrinsically closed harmonic 1-forms of Morse type.

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Cite This Study

García et al. (Sun,) studied this question.

synapsesocial.com/papers/68de5da283cbc991d0a209fd https://doi.org/https://doi.org/10.48550/arxiv.2507.09644

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