Talk:Knot theory
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Recent Advance
[edit]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
[edit]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)
Other Niche Topics Within Knot Theory
[edit]I'd like to add information about planar diagram codes: https://katlas.org/wiki/Planar_Diagrams. Would that fit well enough within this article or would it be better to make a separate article? When should a niche topic be added here or made into a separate article? WhimsicalRuben (talk) 19:32, 6 July 2025 (UTC)
over and under
[edit]In the section Dowker–Thistlethwaite notation, why are three of the pairings both positive, as if both strands of the crossing are over each other? —Antonissimo (talk) 23:10, 19 April 2026 (UTC)
Additivity conjecture is false
[edit]Also posted to Talk:Connected sum:
Hi, I heard today that the additivity conjecture is false according to a new paper: https://arxiv.org/pdf/2506.24088
Video where I heard the news: https://www.youtube.com/watch?v=sGGjWIt28_g
Can someone take a look and see where/if it could be incorporated, please? Thanks. --Kjoonlee 23:48, 23 July 2026 (UTC)
