We say that a given knot J ⊂ S is detected by its knot Floer homology and A-polynomial if whenever a knot K ⊂ S has the same knot Floer homology and the same A-polynomial as J , then K = J . In this paper we show that every torus knot T (p, q) is detected by its knot Floer homology and A-polynomial. We also give a one-parameter family of infinitely many hyperbolic knots in S each of which is de...

It was predicted recently that sufficiently complex knots on a linear wormlike chain can have a metastable size, preventing their spontaneous expansion. We tested this prediction via computer simulations for 7(1) and 10(151) knots. We calculated the equilibrium distributions of knot size S for both knots. By using the umbrella sampling, we were able to obtain the distributions over a wide range...

TImis note is a continuation of [Nl], Wbere we have discusged tbe unknotting number of knots With rspect tía knot diagrams. Wc wilI show that for every minimum-crossing knot-diagram among ah unknotting-number-one two-bridge knot there exist crossings whose exchangeyields tIme trivial knot, ib tbe tbird Tait conjecture is true.

Secreted proteins coded by parasitism genes expressed in esophageal gland cells mediate infection and parasitism of plants by root-knot nematodes. An essential parasitism gene, designated as 16D10, encodes a conserved root-knot nematode secretory peptide that stimulates root growth and functions as a ligand for a plant transcription factor. Plants were engineered to silence this parasitism gene...

Tying secure knots is essential in arthroscopic surgery. A new slip knot for arthroscopic shoulder surgery is described. Locking of the knot is accomplished by pulling the post strand. Knot tying is simple and a low-profile, secure knot is produced.

This paper is a self-contained introduction to the Jones polynomial that assumes no background in knot theory. We define the Jones polynomial, prove its invariance, and use it to tackle two problems in knot theory: detecting amphichirality and finding bounds on the crossing numbers. 1. Preliminaries 1.1. Definitions. For the most part, it is enough to think of a knot as something made physicall...

A p–colouring of a knot K is a surjective homomorphism ρ from its knot group G := π1(S − K) to D2p := {t, s|t2 = sp = 1, tst = sp−1} the dihedral group of order 2p, when p is any odd integer. The pair (K, ρ) is called a p–coloured knot. It is a well-known fact that we can encode ρ as a colouring of arcs of a knot diagram by elements of Zp (the cyclic group of order p), subject to the ‘colouring...

The Ramsey number is known for only a few specific knots and links, namely the Hopf link and the trefoil knot (although not published in periodicals). We establish the lower bound of all Ramsey numbers of any knot to be one greater than its stick number. 1 Background and Definitions The study of Ramsey numbers of knots can be found at the intersection of knot theory and graph theory. 1.1 Knot T...

Numerical simulations indicate that there exist conformations of the unknot, tied on a finite piece of rope, entangled in such a manner, that they cannot be disentangled to the torus conformation without cutting the rope. The simplest example of such a gordian unknot is presented. Knots are closed, self-avoiding curves in the 3-dimensional space. The shape and size of a knot, i.e. its conformat...