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Please check the statement of Reidemeister’s theorem at Reidemeister moves, I was not that happy with the precise wording of the previous version as it made everything look as if it was happening in the plane, rather than indicating that what was happening in the plane mirrored what was happening in 3-dimensions. (Note that there was a discussion on MO, [here], on the proof.)
I’ve put a bit more light hearted stuff at colorability (never know which spelling to use. :-)). crossing number and have started on unknotting number. One day I will get onto the more significant stuff but having this here may be useful to someone.
It’s very useful to me! I’m trying to learn this stuff “on the run” so knowing that there’s someone who knows what’s what and will catch any silly errors I might put in is fantastic.
(You missed a square bracket in your comment: unknotting number)
I am doing the fun bits but when I used to teach this stuff, the students liked this and could often do quite complex invariance proofs as a result of playing around like this. I will do short pages on invertible knots and achiral knots but there are good Wikipedia pages on these so will keep it short.
(I taught it from about 1980 until 2006 - with some gaps, but am limited in my knowledge beyond the course I used to give, together with stuff I picked up talking with Lou Kauffman, who is a true master in more ways than one.)
Finished unknotting number (for the moment).
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