منابع مشابه
Minimal Sets of Reidemeister Moves
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...
متن کاملThe 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...
متن کاملMaking Curves Minimally Crossing by Reidemeister Moves
Let C1 , ..., Ck be a system of closed curves on a triangulizable surface S. The system is called minimally crossing if each curve Ci has a minimal number of selfintersections among all curves C$i freely homotopic to Ci and if each pair Ci , Cj has a minimal number of intersections among all curve pairs C$i , C$j freely homotopic to Ci , Cj respectively (i, j=1, ..., k, i{ j). The system is cal...
متن کاملOn the Necessity of Reidemeister Moves
We show that every knot type admits a pair of diagrams that cannot be made identical without using Reidemeister Ω2-moves. We also show that our proof is compatible with known results for the other move types, in the sense that every knot type admits a pair of diagrams that cannot be made identical without using all of the move types.
متن کاملUnknotting number and number of Reidemeister moves needed for unlinking
Article history: Received 25 April 2011 Received in revised form 11 January 2012 Accepted 11 January 2012
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ژورنال
عنوان ژورنال: Journal of Knot Theory and Its Ramifications
سال: 2015
ISSN: 0218-2165,1793-6527
DOI: 10.1142/s0218216515400064