A polynomial upper bound on Reidemeister moves
نویسندگان
چکیده
منابع مشابه
On 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.
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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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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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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: Annals of Mathematics
سال: 2015
ISSN: 0003-486X
DOI: 10.4007/annals.2015.182.2.3