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The number of Reidemeister Moves Needed for Unknotting
, 2008
"... There is a positive constant c1 such that for any diagram D representing the unknot, there is a sequence of at most 2 c1n Reidemeister moves that will convert it to a trivial knot diagram, where n is the number of crossings in D. A similar result holds for elementary moves on a polygonal knot K embe ..."
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Cited by 38 (11 self)
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There is a positive constant c1 such that for any diagram D representing the unknot, there is a sequence of at most 2 c1n Reidemeister moves that will convert it to a trivial knot diagram, where n is the number of crossings in D. A similar result holds for elementary moves on a polygonal knot K embedded in the 1skeleton of the interior of a compact, orientable, triangulated PL 3manifold M. There is a positive constant c2 such that for each t ≥ 1, if M consists of t tetrahedra, and K is unknotted, then there is a sequence of at most 2 c2t elementary moves in M which transforms K to a triangle contained inside one tetrahedron of M. We obtain explicit values for c1 and c2.
Ordering the Reidemeister moves of a classical knot
 2006), 659–671 (electronic). MR 2240911 (2007d:57010
"... We show that any two diagrams of the same knot or link are connected by a sequence of Reidemeister moves which are sorted by type. 57M25; 57M27 It is one of the founding theorems of knot theory that any two diagrams of a given link may be changed from one into the other by a sequence of Reidemeister ..."
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We show that any two diagrams of the same knot or link are connected by a sequence of Reidemeister moves which are sorted by type. 57M25; 57M27 It is one of the founding theorems of knot theory that any two diagrams of a given link may be changed from one into the other by a sequence of Reidemeister moves. One of the reasons why this result is so crucial to the subject is that it allows one to define a link invariant as an invariant of a diagram which is unchanged under Reidemeister moves.
Ordering the Reidemeister
, 2006
"... pagination and layout may vary from AGT published version ..."
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Ordering the Reidemeister
, 2006
"... pagination and layout may vary from AGT published version ..."
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