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

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.

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