Talk:Reidemeister move

Equivalence of Symmetric cases

It can be shown that the three Reidemeister moves are equivalent to the different symmetric cases. For example, you can use an R2 move to get the reverse of R1 where the twist is in the other direction. The same is true for R2 with the order of the strands reversed, and R3 with the top, middle, or bottom strand moving past the crossing. Does anyone who is good at making images want to make some images for this? Asmeurer (talk ♬ contribs) 16:34, 12 October 2009 (UTC)

Care needed with move Type III

I believe that a picture of the Type III move should emphasise the fact that no part of the knot moves outside the picture. As shown on the main page one might get the impression that the whole knot is 'dragged down' rather than just the single section shown. I don't have an example of why this might matter but I was gently taken to task by a prominent knot theorist for this 'error' when posting a description of Reidemeister's theorem: Reidemeister at theoremoftheday.org (where I believe the picture is as approved by the professionals). Charleswallingford (talk) 19:21, 14 December 2009 (UTC)

What the person was probably complaining about is not specific to the type III move. Anyone that understands the first two moves should understand the same convention holds for the third. Your comments make it clear that in fact you have the very confusion that mysterious knot theorist was trying to allay. The convention to understand the pictures of the moves is that inside a small region that looks exactly as depicted (up to a topological (rubber sheet) distortion of the plane), a move of the indicated type is made inside the region, keeping everything outside the same. Note the endpoints of the strands involved do not move (they can be imagined to lie on the boundary of the small region of modification).

A related, but common, mistake is to have other parts of the diagram inside the modified region. It is important to remember that the region of modification looks exactly as depicted (allowing distortion of course). —Preceding unsigned comment added by 69.86.106.215 (talk) 21:38, 12 December 2010 (UTC)

Reidemeister reference?

Is the Reidemeister reference from the article accurate? "Kurt Reidemeister, Elementare Begründung der Knotentheorie, Abh. Math. Sem. Univ. Hamburg 5 (1926), 24-32". MathSciNet has his earliest publication at 1939, but perhaps MathSciNet isn't very accurate for that period? Rybu (talk) 23:51, 16 June 2010 (UTC)

Update -- In Colin Adams book "The knot book" he cites Reidemeister's 1932 book Knotentheorie. The original manuscript is not referenced by MathSciNet (which leads me to think the citation in this article might be valid) but they do cite a re-print: MR0345089 (49 #9828) Rybu (talk) 23:58, 16 June 2010 (UTC)

Jozef H. Przytycki's "History of Knot Theory" article also cites the above 1932 book. So perhaps the reference should be changed to the 1932 book unless there's something to support the 1926 article -- or if the 1926 article is valid we should at least include a link to the 1932 book as the 1926 article is quite difficult to find. Rybu (talk) 00:03, 17 June 2010 (UTC)