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This article seems to be self-contradictory. There's the paragraph
Two equivalent knots have isomorphic knot groups, so the knot group is a knot invariant and can be used to distinguish between inequivalent knots.
Then in the examples:
The square knot and the granny knot have isomorphic knot groups, yet these two knots are inequivalent.
Perhaps someone familiar with knot theory can clear this up. Ubermichael 00:23, 15 January 2007 (UTC)
One knot may differ from another knot,
Even though their knot groups differ not.
BUT
If a knot has the same group as the not-knotted knot,
Then the knot is not knotted.
I learnt this verse studying mathematics at Warwick University in the early 1970’s. I’m not sure of the exact words, or who came up with it - but it’s in the distinctive teaching style of Professor Ian Stewart. Peter Ells ( talk) 21:11, 5 June 2020 (UTC)
I believe that the left-handed and right-handed trefoil knots have identical knot groups. Peter Ells ( talk) 21:27, 5 June 2020 (UTC)
Could someone add the knot group of the figure eight knot? JackSchmidt ( talk) 19:18, 12 July 2008 (UTC)
![]() | This article is rated Start-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | ||||||||||
|
![]() | It is requested that an image or photograph of Knot group be
included in this article to
improve its quality. Please replace this template with a more specific
media request template where possible.
The Free Image Search Tool or Openverse Creative Commons Search may be able to locate suitable images on Flickr and other web sites. |
This article seems to be self-contradictory. There's the paragraph
Two equivalent knots have isomorphic knot groups, so the knot group is a knot invariant and can be used to distinguish between inequivalent knots.
Then in the examples:
The square knot and the granny knot have isomorphic knot groups, yet these two knots are inequivalent.
Perhaps someone familiar with knot theory can clear this up. Ubermichael 00:23, 15 January 2007 (UTC)
One knot may differ from another knot,
Even though their knot groups differ not.
BUT
If a knot has the same group as the not-knotted knot,
Then the knot is not knotted.
I learnt this verse studying mathematics at Warwick University in the early 1970’s. I’m not sure of the exact words, or who came up with it - but it’s in the distinctive teaching style of Professor Ian Stewart. Peter Ells ( talk) 21:11, 5 June 2020 (UTC)
I believe that the left-handed and right-handed trefoil knots have identical knot groups. Peter Ells ( talk) 21:27, 5 June 2020 (UTC)
Could someone add the knot group of the figure eight knot? JackSchmidt ( talk) 19:18, 12 July 2008 (UTC)