Dynnikov: arc-presentations of links

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August undefined, 2024

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 … 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 …

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Web(2006) Dynnikov. Fundamenta Mathematicae. In the early 90's J. Birman and W. Menasco worked out a nice technique for studying links presented in the form of a closed braid. … WebAs an application, we determine the arc index of infinitely many Kanenobu knots. In particular, we give sharper lower bounds of the arc index of K ( 2 n, − 2 n) by using canonical cabling algorithm and the 2-cable Γ -polynomials. Moreover, we give sharper upper bounds of the arc index of some Kanenobu knots by using their braid presentations. software wireframe

[1005.5263] Essential tori in link complements: impossibility of ...

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 … WebJun 26, 2024 · Grid diagrams were first introduced by Cromwell, Dynnikov and Brunn [2,3,4] and have gained popularity since the use of grids to give a combinatorial definition of … 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 … software wisp

The problem of detecting the satellite structure of a link by …

Arc presentations of Montesinos links Journal of Knot …

WebNov 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 … slow ride allstateWebSep 4, 2024 · 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 ... software wireframes

"WebWe show that a minimal rectangular diagram maximizes the Thurston-Bennequin number for the corresponding Legendrian links. We prove the Jones conjecture on the invariance of the algebraic number of crossings of a minimal braid representing a given link. ... I. A. Dynnikov, Arc-presentations of links: monotonic simplification, Fund. Math. 190 ... " - Dynnikov: arc-presentations of links

Dynnikov: arc-presentations of links

Unknotting rectangular diagrams of the trivial knot by exchanging …

WebIvan DYNNIKOV Cited by 988 of Lomonosov Moscow State University, Moscow (MSU) Read 109 publications Contact Ivan DYNNIKOV ... Arc-presentations of links. … WebJun 21, 2010 · We give an introduction to the work of Dynnikov who discovered the key use of arc--presentations to solve the problem of finding a way to detect the unknot directly from a diagram of the knot.

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WebNov 3, 2024 · For instance, Dynnikov diagrams with vertical and horizontal lines can be used to represent and solve knots; these are called “arc-presentations” and their complexity is equivalent to the number of the vertical lines of the diagram and, following a theorem by Dynnikov , every knot has an arc-presentation (Fig. 17.4). WebCiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): Arc-presentations of links were introduced by J.Birman and W. Menasco, some basic …

WebHere we exhibit a further development of that technique and of the theory of arc-presentations, and prove that any arc-presentation of the unknot admits a (non-strictly) … 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.

WebA. Dynnikov, Three-page link presentation and an untangling algorithm, in Proc. of the International Conference Low-Dimensional Topology and Combinatorial Group Theory, ... Google Scholar; 9. I. A. Dynnikov, Arc-presentations of links: Monotonic simplification, Fund. Math. 190 (2006) 29–76. WebArc-presentations of links. Monotonic simpliﬁcation I.A.Dynnikov Dept. of Mech. & Math. Moscow State University Moscow 119992 GSP-2, Russia e-mail: …

Web$\begingroup$ 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. …

http://homepages.math.uic.edu/~kauffman/henrichkauffman.pdf slow ride american idolWebJul 10, 2024 · We introduce a new very large family of transformations of rectangular diagrams of links that preserve the isotopy class of the link. We provide an example when two diagrams of the same complexity are related by such a transformation and are not obtained from one another by any sequence of “simpler” moves not increasing the … slow ride artistWebAug 13, 2015 · I. A. Dynnikov, Three-page link presentation and an untangling algorithm, In: "Proc. of the International Conference Low-Dimensional Topology and Combinatorial Group Theory, Chelyabinsk, July 31 ... slow ride albumWebAug 21, 2002 · Title: Arc-presentations of links. Monotonic simplification. Authors: Ivan Dynnikov. Download PDF Abstract: We prove that any arc-presentation of the unknot admits a monotonic simplification by elementary moves; this yields a simple algorithm for recognizing the unknot. We obtain similar results for split links and composite links. software with a poor reputationhttp://homepages.math.uic.edu/~kauffman/henrichkauffman.pdf slow ride bakery incWebDec 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 ... slow ride argument lyricsWebEssential 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- slowride bakery big chocolate cookie