This paper shows that the complex projective plane 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.
Matthew Stover (Fri,) studied this question.