Dynnikov: arc-presentations of links
WebAug 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 ... 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.
Dynnikov: arc-presentations of links
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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 ... 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) …
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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 … 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
WebJul 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 …
WebAug 21, 2002 · A few years later P. Cromwell adapted Birman-Menasco's method for studying so-called arc-presentations of links and … how many chicken girls seasonWebMay 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 … high school girl divingWebNov 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). high school girl framed for bullyingWebTY - 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 … high school girl fightingWebPresentations ** SCHEDULING RESOURCES ** Schools Translate. Back to Top. Important Contacts. Contact Information Main Office: 703-957-4400 School Counseling: … high school girl dating teacherWebIvan 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 high school girl fights in classroomWebEssential 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- how many chicken legs in a pound