Does anyone know if it is possible to construct a(adsbygoogle = window.adsbygoogle || []).push({}); compact3-manifold with no boundary and negative curvature? I ask this question in the Cosmology sub-forum because I see in various writings of cosmologists that it is often taken for granted that a negatively curved Universe must be infinite.

I think it can be proved, though I have not actually seen a proof, that it is impossible for 2-manifolds. Can anyone shed light on this question?

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# Compact 3-manifolds of Negative Curvature

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