Talk:Knot theory

Knot Equivalence
The definition given there appears to be wrong. Actually it is defining "isotopy" rather than "ambient isotopy" and it is well-known (see e.g. the first pages of Burde-Zieschang: "Knots") that isotopy does not imply ambient isotopy. (Besides the map would only have to be injective level-wise, and moreover, of course it can not be injective as a map on [0,1] but rather on S^1.)--Kamsa Hapnida (talk) 12:05, 8 June 2015 (UTC) I have replaced that by a correct definition now.--Kamsa Hapnida (talk) 12:14, 8 June 2015 (UTC)

Assessment comment
{{Substituted comment|length=363|lastedit=20090315222649|comment=History section could use some more references, especially to historically important papers. -- Jitse Niesen (talk) 05:08, 26 April 2007 (UTC)

Knot definition
The definition says that a knot is an injective continuous function K:[0,1]->R^3 with K(0)=K(1), but really K isn't injective if K(0)=K(1). — Preceding unsigned comment added by 2601:199:301:1691:C4E4:4553:198C:1587 (talk) 20:11, 12 January 2017 (UTC)


 * History has been spun off into its own article, since people found it a bit distracting and long. --C S (talk) 22:26, 15 March 2009 (UTC)}}

Substituted at 21:20, 29 April 2016 (UTC)

Recent Advance
This is not(!) my area but I came across this which sounds like a big deal: https://www.maths.ox.ac.uk/node/38304 Relates to "unknot" equivalence determination in near polynomial time by M Lackenby. Billymac00 (talk) 13:29, 3 February 2021 (UTC)
 * That's interesting! I added a mention of this announcement, both here and on Lackenby's page. Turgidson (talk) 15:15, 3 February 2021 (UTC)

Knot Theory in Higher Dimensions
Not sure where to raise this, but the subheader in the article begins to explain how to do it, and then sort of cuts short with "it's very technical". I feel as though this section should be revised, either to be more concise, or more precise. Also, a citation would be nice for those of us who want to learn how its done. — Preceding unsigned comment added by 203.211.110.97 (talk) 12:35, 29 May 2021 (UTC)