Unknotting number and number of Reidemeister moves needed for unlinking
نویسندگان
چکیده
Article history: Received 25 April 2011 Received in revised form 11 January 2012 Accepted 11 January 2012
منابع مشابه
A Lower Bound for the Number of Reidemeister Moves for Unknotting
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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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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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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After proving a theorem about the general formulae for the signature of alternating knot and link families, we distinguished all families of knots obtained from generating alternating knots with at most 10 crossings and alternating links with at most 9 crossings, for which the unknotting (unlinking) number can be confirmed by using the general formulae for signatures.
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We study the number of Reidemeister type III moves using Fox n-colorings of knot diagrams.
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تاریخ انتشار 2012