Dynnikov: arc-presentations of links

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August undefined, 2024

WebSep 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 ... 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 …

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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 … 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. iphone not sending photos

EUDML Arc-presentations of links: Monotonic simplification

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- 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 ... iphone not sending pictures in text messages

Arc-presentations of links. Monotonic simpliﬁcation

Algorithmic computation of the crossing number of a link: new …

Webpowerful 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 ... WebIvan DYNNIKOV Cited by 988 of Lomonosov Moscow State University, Moscow (MSU) Read 109 publications Contact Ivan DYNNIKOV ... Arc-presentations of links. Monotonic simplification. Article ... orange county clerk of clerks orlando flWebIvan 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 orange county clerk of court budget

"Webpowerful 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 " - Dynnikov: arc-presentations of links

Dynnikov: arc-presentations of links

$A. Kazantsev Abstract. arXiv:1005.5263v2 [math.GT] 4 Oct …$

http://homepages.math.uic.edu/~kauffman/henrichkauffman.pdf 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 ...

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WebCiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): Arc-presentations of links were introduced by J.Birman and W. Menasco, some basic … WebBirman and Menasco introduced arc-presentation of knots and links in [1], and Cromwell formulated it in [2]. Dynnikov pointed out in [3] and [4] that Cromwell’s argument in [2] 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.

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).

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 … WebAug 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.

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 ...

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 ... iphone not sending or receiving textsWebJun 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. iphone not setting uphttp://homepages.math.uic.edu/~kauffman/henrichkauffman.pdf orange county clerk of court division 39WebTY - JOUR AU - I. A. Dynnikov TI - Arc-presentations of links: Monotonic simplification JO - Fundamenta Mathematicae PY - 2006 VL - 190 IS - 1 SP - 29 EP - 76 AB - In the … orange county clerk of court californiaWeb(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. … orange county clerk of court clerkWebJul 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 … iphone not sending sms text messagesWebA. 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. orange county clerk of court civil division