User talk:71.255.103.20

"hyperbolic links" and the (non-)hyperboliity of the "Hopf Link"?
While I hesitate to edit these myself [I'm a professional mathematician* whose work is mentioned on many Wikipedia pages, but have no "page of my own" – and I actually have some trepidation in the event such a page may someday be created, since then I'd worry about what it says: would that be paparazzi-phobia?!? ;-], I just noticed a possible inconsistency in the two Wikipedia pages noted above.

Perhaps one wants to add the terms "complete" and especially "finite volume" to the hyperbolic metric on a link complement in S^3 in order for that link to be considered hyperbolic?

Otherwise, the Hopf Link might also be considered hyperbolic, since its complement is homeomorphic to R\timesS^1\timesS^1, which does carry a complete hyperbolic metric with *infinite* volume (it's the quotient of H^3 by a rank-2 parabolic subgroup of Isom^+(H^)=PSL(2,C) with one cusp end and one "big" end – in the upper-halfpace model, this subgroup corresponds to translations by a lattice in the ideal boundary plane).

— Rob Kusner, UMassAmherst , 

71.255.103.20 (talk) 04:07, 28 June 2021 (UTC)