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Contradiction?
editThis 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)
- a pretty late reply but the point is that while it's an invariant, it's not a complete invariant. two equivalent knots have the same knot group but the converse is not true in general. Mct mht 23:34, 17 October 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)
Figure eight
editCould someone add the knot group of the figure eight knot? JackSchmidt (talk) 19:18, 12 July 2008 (UTC)
- Added the knot group for fig. 8 LkNsngth (talk) 23:59, 14 July 2008 (UTC)
- Excellent, thanks! JackSchmidt (talk) 01:00, 15 July 2008 (UTC)