Dynnikov: arc-presentations of links
WebBirman and Menasco introduced arc-presentation of knots and links in [], and Cromwell formulated it in [].Dynnikov pointed out in [] and [] that Cromwell’s argument in [] almost shows that any arc-presentation of a split link can be deformed into one which is ‘ ‘ visibly split” by a finite sequence of exchange moves. He also showed that any arc … WebLemma 2. Suppose a knot (or link) diagram Kin Morse form has cr(K) crossings and b(K) maxima. Then there is an arc–presentation L K of K with complexity. 5 Figure 7. ... Theorem 3 (Dynnikov). If L is an arc–presentation of the unknot, then there exists a finite sequence of exchange and destabilization moves L→ L1 → L2 → ··· → L ...
Dynnikov: arc-presentations of links
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WebDec 6, 2024 · A knot is circle piecewise-linearly embedded into the 3-sphere. The topology of a knot is intimately related to that of its exterior, which is the complement of an open regular neighborhood of the ... WebMay 28, 2010 · In a recent work "Arc-presentation of links: Monotonic simplification" Ivan Dynnikov showed that each rectangular diagram of the unknot, composite link, or split link can be monotonically simplified into a trivial, composite, or split diagram, respectively. The following natural question arises: Is it always possible to simplify monotonically a …
WebJan 1, 2011 · In a recent work "Arc-presentation of links: Monotonic simplification", Dynnikov shows that each rectangular diagram of the unknot, composite link, or split link can be monotonically simplified ... WebIn this paper, we prove a theorem that allows one to evaluate the Heegaard-Floer homology of a link with trivial component added through the Heegaard-Floer homology of the initial …
WebDynnikov, Ivan Abstract We prove that any arc-presentation of the unknot admits a monotonic simplification by elementary moves; this yields a simple algorithm for … WebEssential tori in link complements: detecting the satellite structure by monotonic simplification A. Kazantsev1 Abstract. In a recent work “Arc-presentation of links: Monotonic sim-plification” Ivan Dynnikov showed that each rectangular diagram of the un-knot, composite link, or split link can be monotonically simplified into a triv-
WebIvan DYNNIKOV Cited by 988 of Lomonosov Moscow State University, Moscow (MSU) Read 109 publications Contact Ivan DYNNIKOV ... Arc-presentations of links. …
WebJul 6, 2016 · For now, we focus our attention on arc–presentations. Proposition 1 (Dynnikov). Every knot has an arc–presentation. Any two arc–presentations of the same knot can be related to each other by a finite sequence of elementary moves , pictured in Figs. 13 and 14. tails from sonic the hedgehog coloring pagesWebCiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): Arc-presentations of links were introduced by J.Birman and W. Menasco, some basic … twin cities led bulb christmas lightsWebpowerful result proven by Dynnikov in [4] regarding arc-presentations of knots. Arc-presentations are special types of rectangular diagrams, i.e., knot diagrams that are composed entirely of horizontal and vertical lines. Here, we provide an overview of the theory of arc-presentations. In Figure6, we give an example of a rectangular diagram tails from sonic the hedgehog toysWeb$\begingroup$ Dynnikov's paper "Arc-presentations of links. Monotonic simplification" (arXiv:0208153) was mentioned several times in answers to the unknot recognition question. The algorithm in that paper can also recognize split links and hence unlinks, and it does so without ever increasing the size of the diagram, but I don't think there are any good (e.g. … twin cities light bulbsWebIvan Dynnikov discovered it when he was working on his manuscript [7], where he established two theorems about arc presentations of links which are similar to the two theorems that we had proved for closed braid presentations in [3]. His proof was a modification of our proof to new tails from sonic the hedgehog flyinghttp://math.columbia.edu/~jb/slvcb-iv-erratum.pdf tails from the ark honk if your specialWebNov 16, 2024 · For the new presentation we define moves and rewrite the criterion of realizability. ... I. Dynnikov, “Arc-presentations of links: monotonic simplification,” Fund. Math. 190, 29–76 ... M. Ozawa, “Edge number of knots and links,” arXiv:math.GT/0705.4348 (2007). Google Scholar Download references. Author … tails from the city cleveland