A hyperbolic 4-orbifold with underlying space ℙ²

2025/06/13 by Matthew Stover, Stover, Matthew
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2506.11667

openalex publication_date 2025/06/13 · openalex created_date 2025/10/11 · openalex updated_date 2026/07/28

Abstract

This paper shows that the complex projective plane ℙ² can be realized as the underlying space for a closed hyperbolic 4-orbifold. This is the first example of a closed hyperbolic 4-orbifold whose underlying space is symplectic, which is related to the open question as to whether or not closed hyperbolic 4-manifolds can admit symplectic structures.

Citations

• Adjunction inequalities and the Davis hyperbolic four-manifold
• Hyperbolic Manifolds, Harmonic Forms, and Seiberg-Witten Invariants

Related

• Orbifolds and orbibundles in complex hyperbolic geometry
• On a class of symplectic 4-orbifolds with vanishing canonical class
• Resolution of 4-dimensional symplectic orbifolds
• Projective structures on a hyperbolic 3-orbifold
• Symplectic packing in dimension 4