A hyperbolic $4$-orbifold with underlying space $\mathbb{P}^2$
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911599556558848 |
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| author | Stover, Matthew |
| author_facet | Stover, Matthew |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_11667 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A hyperbolic $4$-orbifold with underlying space $\mathbb{P}^2$ Stover, Matthew Geometric Topology Differential Geometry 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. |
| title | A hyperbolic $4$-orbifold with underlying space $\mathbb{P}^2$ |
| topic | Geometric Topology Differential Geometry |
| url | https://arxiv.org/abs/2506.11667 |