Progress on the paper by Hass and Lagarias on Reidemeister moves needed for unknotting

Asked Jul 08 '21 at 20:43

Active Jul 09 '21 at 08:21

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Has any progress been made on the findings of 2001 paper by Joel Hass and Jeffrey C. Lagarias? The paper is

Joel Hass and Jeffrey C. Lagarias, The number of Reidemeister moves needed for unknotting, J. Amer. Math. Soc. 14 (2001), 399-428, doi:10.1090/S0894-0347-01-00358-7, arXiv:math/9807012 .

edited Jul 09 '21 at 08:21

YCor

asked Jul 08 '21 at 20:43

Aditya_Srinath

Could you clarify the question? Are you asking for a survey of the general area related to the article's theme? If so, that seems overly broad. – Igor Belegradek Jul 08 '21 at 21:29
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Yes, for example, A Polynomial Upper Bound on Reidemeister Moves by Marc Lackenby in the Annals of Mathematics https://www.jstor.org/stable/24523342 – Will Sawin Jul 08 '21 at 21:33
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There is no need to close this question. It's not doing any harm. Worse to worse, this question will remain overly broadly formulated, and thus won't get a (good) answer. But most likely, the OP will edit the question to make it more well-focussed. – André Henriques Jul 08 '21 at 21:34
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Unfortunately, MathOverflow is crawling with vigilantes. – Daniel Asimov Jul 08 '21 at 23:30
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See also: Are there any very hard unknots?, and Number of the Reidemeister moves needed to transform one diagram into another one. Both mention Lackenby's result. – Joseph O'Rourke Jul 08 '21 at 23:32
The answer to the question in the title is yes. – Ryan Budney Jul 09 '21 at 08:06
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Behind the expensive AMS paywall you can get on MathSciNet the list of the (now 33) published papers quoting this paper. With no paywall, ZBmath finds 26 quoting papers. Google Scholar finds more than 100 quotations on the web. – YCor Jul 09 '21 at 08:18
More recently, Lackenby has announced even more spectacular results: https://www.maths.ox.ac.uk/node/38304 – HJRW Jul 11 '21 at 14:36

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