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Aug 31, 2010 at 23:51 comment added Ryan Budney In some sense hyperbolic $3$-manifolds do have names. Their fundamental group functions as a name, since the isomorphism problem is decidable for them. I think in some way the mystery is more the other-way around -- instead of assigning names we want a "phone book". Like: I want a non-repeating list of all hyperbolic 3-manifolds with volume less than 20, how do I generate that list efficently? Similarly, "is $\sqrt{71\sqrt{11}}$ the volume of a hyperbolic 3-manifold?"
Aug 31, 2010 at 18:28 history edited Bruno Martelli CC BY-SA 2.5
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Aug 31, 2010 at 17:27 history answered Bruno Martelli CC BY-SA 2.5