Abstract
Abstract 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 Twain
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