http://math.columbia.edu/~jb/slvcb-iv-erratum.pdf 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.

(PDF) Unknotting Unknots - ResearchGate

WebScience researcher, writer, and editor working in scientific publishing. Executive Editor of Open Access Cancer Research Journals at SAGE Publishing. Background in the life … 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 … did hathor have any children

arXiv:1006.4176v4 [math.GT] 4 Nov 2011

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 ... WebLet L be a Montesinos link M (− p, q, r) with positive rational numbers p, q and r, each less than 1, and c (L) the minimal crossing number of L. Herein, we construct arc presentations of L with c (L), c (L) − 1 and c (L) − 2 arcs under some conditions for p, q and r. Furthermore, we determine the arc index of infinitely many Montesinos ... 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. did haters back off get canceled