Timeline for Effective contraction of a loop. Reference or a simple proof?
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| Sep 22, 2010 at 11:51 | comment | added | Bill Thurston | I believe the length of tracks is a noncomputable function even for triangulations of the 4-ball, by the same line of reasoning. Of course for any single triangulation of a simply-connected manifold it's bounded, as Ivanov noted in his answer, but shrinking length can be larger than any computable function for contractible curves in non-simply-connected manifolds. Note that for triangulated 3-manifolds, Haken developed methods that transform the question to integer linear programming, whose solutions have explicit bounds in terms of the number of simplices. | |
| Sep 22, 2010 at 0:04 | comment | added | Benoît Kloeckner | The bound on the length used to contract loops could exist and be a non-computable function of $M$. | |
| Sep 21, 2010 at 22:28 | history | answered | Ian Agol | CC BY-SA 2.5 |