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For this knot with DT code -8 16 28 14 -2 6 -20 10 24 -32 -12 -30 18 -22 4 -26 I received an error message from Knot Finder: "KnotFinder encountered an unknown error."

I also tried SnapPy (using the Plink Editor and sending the information to SnapPy). The command M.identify() yielded: [].

I suspect that the knot is 16n847920. Who can help to identify this knot and why does it produce the above results? Thanks.

enter image description here

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    $\begingroup$ I think SnapPy's identify method doesn't search through 16-crossing knots because there are too many of them, but if you set "M=Manifold('DT:[(-8,16,28,14,-2,6,-20,10,24,-32,-12,-30,18,-22,4,-26)]')" then "Manifold('16n847920').is_isometric_to(M)" should still return True. $\endgroup$
    – Steven Sivek
    Commented Mar 14, 2023 at 22:13
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    $\begingroup$ Hi Steven, thanks. This check works. As a remark I would like to add that Knot Finder recognises the knot 16n847920 with other input and returns the minimal DT code 6 -10 28 30 -14 -4 18 -8 22 12 -26 16 -32 -20 2 -24 for it. The message "unknown error" only occurs for some diagram inputs. $\endgroup$
    – Christoph Lamm
    Commented Mar 15, 2023 at 7:44
  • $\begingroup$ @StevenSivek - Perhaps add that comment as a short answer which can then be accepted? $\endgroup$
    – Sam Nead
    Commented Mar 15, 2023 at 11:06

2 Answers 2

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Turning my comment into an answer, I think SnapPy's identify method doesn't search through 16-crossing knots because there are too many of them, but if you think you know which knot you have then SnapPy can still verify your guess:

In[1]: M=Manifold('DT:[(-8,16,28,14,-2,6,-20,10,24,-32,-12,-30,18,-22,4,-26)]')

In[2]: Manifold('16n847920').is_isometric_to(M)

Out[2]: True
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  • $\begingroup$ Thanks. This is already helpful. There are two remaining topics: 1) Does anyone find an identification of the above knot when we do not already have a candidate for it? (Which other tools might be successful in this case?) 2) For somebody with a local installation of Knotscape: Does the same error message occur as in Knot Finder? (And can the cause of the error message be located in the code?) $\endgroup$
    – Christoph Lamm
    Commented Mar 15, 2023 at 11:43
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    $\begingroup$ For (1), you could just iterate through NonalternatingKnotExteriors() in SnapPy. Volume computations are fast, so for every knot K whose volume was within 0.001 of M.volume(), I used M.is_isometric_to(K) to compare them. It found 16n847920 in just over 45 minutes, which is fine for isolated examples but I'd also like to know if there's a faster way. $\endgroup$
    – Steven Sivek
    Commented Mar 15, 2023 at 14:30
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I just tried Knotscape on this knot and it immediately identified it as 16n847920.

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    $\begingroup$ Welcome to mathoverflow! $\endgroup$
    – Sam Nead
    Commented Sep 28, 2023 at 21:25
  • $\begingroup$ Hi Morwen! Glad to "see" you here. $\endgroup$
    – Ryan Budney
    Commented Sep 29, 2023 at 2:39

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