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arXiv · 2507.09644

Topology of singular foliations of closed 1-forms on orbifolds

Daniel Lopez Garcia·Fabricio Valencia
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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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Daniel Lopez Garcia, Fabricio Valencia. 2026-04-03. Topology of singular foliations of closed 1-forms on orbifolds. https://arxiv.org/abs/2507.09644

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