MINIMAL UNKNOTTING SEQUENCES OF REIDEMEISTER MOVES CONTAINING UNMATCHED RII MOVES
نویسندگان
چکیده
منابع مشابه
The Number of Reidemeister Moves Needed for Unknotting the Number of Reidemeister Moves Needed for Unknotting
There is a positive constant c 1 such that for any diagram D representing the unknot, there is a sequence of at most 2 c 1 n 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 polyg-onal knot K embedded in the 1-skeleton of the interior of a compact, orientable, triangulated PL 3-manifold M...
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It is well known that any two diagrams representing the same oriented link are related by a finite sequence of Reidemeister moves Ω1, Ω2 and Ω3. Depending on orientations of fragments involved in the moves, one may distinguish 4 different versions of each of the Ω1 and Ω2 moves, and 8 versions of the Ω3 move. We introduce a minimal generating set of four oriented Reidemeister moves, which inclu...
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Article history: Received 25 April 2011 Received in revised form 11 January 2012 Accepted 11 January 2012
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A knot is an embedding of a circle S in a 3-manifold M , usually taken to be R or S. In the 1920’s Alexander and Briggs [2, §4] and Reidemeister [23] observed that questions about ambient isotopy of polygonal knots in R can be reduced to combinatorial questions about knot diagrams. These are labeled planar graphs with overcrossings and undercrossings marked, representing a projection of the kno...
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How many Reidemeister moves do we need for unknotting a given diagram of the trivial knot? Hass and Lagarias gave an upper bound. We give an upper bound for deforming a diagram of a split link to be disconnected. On the other hand, the absolute value of the writhe gives a lower bound of the number of Reidemeister I moves for unknotting. That of a complexity of knot diagram “cowrithe” works for ...
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ژورنال
عنوان ژورنال: Journal of Knot Theory and Its Ramifications
سال: 2012
ISSN: 0218-2165,1793-6527
DOI: 10.1142/s021821651250099x