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A hyperbolic $4$-orbifold with underlying space $\mathbb{P}^2$
[Un orbifold hyperbolique de dimension $4$ avec l’espace sous-jacent $\mathbb{P}^2$]
Matthew Stover1
1Temple University, USA
Comptes Rendus. Mathématique, Volume 364 (2026), pp. 279-286

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.

Ce papier montre que le plan projectif complexe $\mathbb{P}^2$ peut être réalisé comme l’espace sous-jacent d’un orbifold hyperbolique fermé de dimension $4$. Il s’agit du premier exemple d’un orbifold hyperbolique fermé de dimension $4$ dont l’espace sous-jacent est symplectique, ce qui est lié à la question ouverte de savoir si les variétés hyperboliques fermées de dimension $4$ peuvent admettre des structures symplectiques.

Reçu le :
Révisé le :
Accepté le :
Publié le :
DOI : 10.5802/crmath.828
Classification : 57R18
Keywords: Hyperbolic $4$-orbifolds
Mots-clés : Orbifolds hyperboliques de dimension $4$

Matthew Stover  1

1 Temple University, USA
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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     title = {A hyperbolic $4$-orbifold with underlying space~$\mathbb{P}^2$},
     journal = {Comptes Rendus. Math\'ematique},
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Matthew Stover. A hyperbolic $4$-orbifold with underlying space $\mathbb{P}^2$. Comptes Rendus. Mathématique, Volume 364 (2026), pp. 279-286. doi: 10.5802/crmath.828

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