Timeline for How do I efficiently find a sequence of Reidemeister moves between equivalent link diagrams?
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
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| Dec 4, 2014 at 9:06 | vote | accept | Idonknow | ||
| Nov 6, 2013 at 18:13 | answer | added | Ian Agol | timeline score: 5 | |
| Nov 6, 2013 at 17:11 | comment | added | Joel David Hamkins | Perhaps this question should be considered as a duplicate of Gowers's question (see link in Ben Barber's comment), which has many outstanding answers related exactly to this question. | |
| Nov 6, 2013 at 16:30 | answer | added | Anonymous | timeline score: 7 | |
| Nov 6, 2013 at 16:20 | history | edited | Daniel Moskovich | CC BY-SA 3.0 |
tags edited, question clarified, title editted
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| Nov 6, 2013 at 16:16 | comment | added | Daniel Moskovich | I've posted on this topic here: ldtopology.wordpress.com/2013/10/13/… | |
| Nov 6, 2013 at 16:14 | comment | added | Ryan Budney | For trivial, hyperbolic and torus links there's certain anecdotal evidence that supports the idea there is a flow to a more-or-less canonical position (up to conformal diffeo). But this would be in terms of a physical knot rather than diagram crossing changes. But for more complicated links there does not appear to be natural ways to relate the position of one to the position of another. You might want to try using software like "knotscape" to play around with these flows. | |
| Nov 6, 2013 at 16:12 | review | Close votes | |||
| Nov 6, 2013 at 17:35 | |||||
| Nov 6, 2013 at 15:30 | comment | added | Joel David Hamkins | And in the context of Borel equivalence relations, it seems that knot equivalence is very high in the hierarchy under Borel reducibility. See logic.univie.ac.at/2012/Talk_10-04_a.html | |
| Nov 6, 2013 at 15:29 | comment | added | Ben Barber | You might like to look at this old question of Gowers on whether there are trivial knots that are tricky to "undo". mathoverflow.net/questions/53471/… | |
| Nov 6, 2013 at 15:26 | comment | added | Joel David Hamkins | See gilkalai.wordpress.com/2012/04/10/…, which explains that Greg Kuperberg has proved under GRH that the special case of determining if a knot is trivial is in NP. This by itself doesn't seem to answer the question of finding the moves when it is known that two knots are equivalent, but it is clearly related. Greg's paper: front.math.ucdavis.edu/1112.0845 | |
| Nov 6, 2013 at 15:19 | comment | added | Joel David Hamkins | Perhaps we could focus your question by asking for a feasible procedure, rather than merely a computational procedure (since otherwise one could simply undertake an exhaustive search). So a related question might be: what is the computational complexity of determining knot equivalence? Is it NP complete? How complex is it to find the witnessing sequence of moves? | |
| Nov 6, 2013 at 15:17 | review | First posts | |||
| Nov 6, 2013 at 15:18 | |||||
| Nov 6, 2013 at 14:57 | history | asked | Idonknow | CC BY-SA 3.0 |