The Signature of Cusped Hyperbolic 4-Manifolds

In this note we show that every integer is the signature of a non-compact, oriented, hyperbolic $4$-manifold of finite volume and give some partial results on the "geography" of such manifolds. The main ingredients are a theorem of Long and Reid, and the explicit construction of a hyperbolic 24-cell manifold with some special topological properties.Few things are harder to put up with than the annoyance of a good example.- Mark Twai