A hyperbolic $4$-orbifold with underlying space $\mathbb{P}^2$

Matthew Stover

A hyperbolic $4$-orbifold with underlying space $\mathbb{P}^2$

Geometric Topology 2026-04-20 v2 Differential Geometry

Authors: Matthew Stover

Abstract

This paper shows that the complex projective plane $\mathbb{P}^2$ 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.

Keywords

hyperbolic geometry symplectic geometry smooth 4-manifolds

Cite

@article{arxiv.2506.11667,
  title  = {A hyperbolic $4$-orbifold with underlying space $\mathbb{P}^2$},
  author = {Matthew Stover},
  journal= {arXiv preprint arXiv:2506.11667},
  year   = {2026}
}

Comments

To appear in C. R. Math. Acad. Sci. Paris

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