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

Matthew Stover

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arXiv · 2506.11667

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

Matthew Stover

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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.

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Matthew Stover. 2025-06-13. A hyperbolic $4$-orbifold with underlying space $\mathbb{P}^2$. https://arxiv.org/abs/2506.11667

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