Can bilipschitz models of hyperbolic 3-manifolds be made effective? - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-18T08:01:52Z http://mathoverflow.net/feeds/question/110875 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/110875/can-bilipschitz-models-of-hyperbolic-3-manifolds-be-made-effective Can bilipschitz models of hyperbolic 3-manifolds be made effective? bb 2012-10-28T04:52:42Z 2012-10-29T04:39:58Z <p>In their proof of the Ending Lamination Conjecture, Brock, Canary, and Minsky prove existence of bilipschitz models of hyperbolic 3-manifolds (homeomorphic to a surface times \$\mathbb{R}\$) depending only on the topology and ending invariants of the manifold.</p> <p>(See <a href="http://arxiv.org/abs/math/0412006" rel="nofollow">The classification of Kleinian surface groups, II: The Ending Lamination Conjecture</a> and <a href="http://www.ams.org/mathscinet-getitem?mr=2630036" rel="nofollow">The classification of Kleinian surface groups. I. Models and bounds</a>)</p> <p>Their proof is non-constructive, so the bilipschitz constants cannot be computed from their proof.<br> Are the bilipschitz constants close to being computable from their proof? In other words is it "easy" to see what steps in their proof are non-constructive and whether these steps can be made effective?</p> http://mathoverflow.net/questions/110875/can-bilipschitz-models-of-hyperbolic-3-manifolds-be-made-effective/110892#110892 Answer by unknown (google) for Can bilipschitz models of hyperbolic 3-manifolds be made effective? unknown (google) 2012-10-28T10:12:26Z 2012-10-29T04:39:58Z <p>See Bowditch: <a href="http://msp.org/pjm/2007/232-1/pjm-v232-n1-p01-s.pdf" rel="nofollow">link text</a> Systems of bands in hyperbolic 3-manifolds</p> <p>with an approach to the Brock-Canary-Minsky Theorem (though not through their model manifold) that is, in principle, effective. Though I am not aware of an explicit algorithmic realization.</p>