Topology of singular foliations of closed 1-forms on orbifolds

2025/07/13 by Daniel López García, Lopez-Garcia, Daniel, Fabricio Valencia +1 · 1 citation
Mathematics · #Geometric and Algebraic Topology #Geometric Analysis and Curvature Flows #Algebraic Geometry and Number Theory

paper · pdf · doi:10.48550/arxiv.2507.09644

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.

Citations

• Novikov type inequalities for orbifolds
• Morse theory on Lie groupoids
• Introduction to orbifolds
• The Orbit Space and Basic Forms of a Proper Lie Groupoid
• Geometrization of Three-Dimensional Orbifolds via Ricci Flow
• Geometry of orbit spaces of proper Lie groupoids
• Equivariant cohomology for Hamiltonian torus actions on symplectic orbifolds
• Differentiable Stacks and Gerbes
• Chern character for twisted K-theory of orbifolds
• Morse theory of harmonic forms
• Hamiltonian torus actions on symplectic orbifolds and toric varieties

Cited by

• Lyapunov 1-forms on orbifolds

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• Foliations with Morse singularities
• Closed meromorphic 1-forms
• Codimension one foliations with Bott-Morse singularities I
• Orbifolds, geometric structures and foliations. Applications to harmonic maps
• On smooth foliations with Morse singularities