despite advances in different techniques of suturing and their alternatives, controversies exist in their indications in laparoscopic surgeries. due to difficulties exist with laparoscopic suturing knots the hemolock technique was introduced in this study. the objective of this study was to compare resistance among extracorporeal meltzer and roeder knot and hemolock in laparoscopic surgery. in ...

We report the stereoselective synthesis of a left-handed trefoil knot from a tris(2,6-pyridinedicarboxamide) oligomer with six chiral centers using a lanthanide(III) ion template. The oligomer folds around the lanthanide ion to form an overhand knot complex of single handedness. Subsequent joining of the overhand knot end groups by ring-closing olefin metathesis affords a single enantiomer of t...

The knot nomenclature in common use, summarized in Rolfsen's knot table [Rolfsen (1990) Knots and Links, American Mathematical Society], was not originally designed to distinguish between mirror images. This ambiguity is particularly inconvenient when studying knotted biopolymers such as DNA and proteins, since their chirality is often significant. In the present article, we propose a biologica...

We study the 2-loop part of the rational Kontsevich integral of a knot in an integer homology sphere. We give a general formula which explains how the 2-loop part of the Kontsevich integral of a knot changes after surgery on a single clasper whose leaves are not linked to the knot. As an application, we relate this formula with a conjecture of L. Rozansky about integrality of the 2-loop polynom...

This paper introduces the concept of Fourier knot. A Fourier knot is a knot that is represented by a parametrized curve in three dimensional space such that the three coordinate functions of the curve are each finite Fourier series in the parameter. That is, the knot can be regarded as the result of independent vibrations in each of the coordinate directions with each of these vibrations being ...

Symplectic knot spaces are the spaces of symplectic subspaces in a symplectic manifold M . We introduce a symplectic structure and show that the structure can be also obtained by the symplectic quotient method. We explain the correspondence between coisotropic submanifolds in M and Lagrangians in the symplectic knot space. We also define an almost complex structure on the symplectic knot space,...

The unknotting number of a knot is bounded from below by its slice genus. It is a well-known fact that the genera and unknotting numbers of torus knots coincide. In this note we characterize quasipositive knots for which the genus bound is sharp: the slice genus of a quasipositive knot equals its unknotting number, if and only if the given knot appears in an unknotting sequence of a torus knot.

We exhibit a knot P in the solid torus, representing a generator of first homology, such that for any knot K in the 3-sphere, the satellite knot with pattern P and companion K is not smoothly slice in any homology 4-ball. As a consequence, we obtain a knot in a homology 3-sphere that does not bound a piecewise-linear disk in any homology 4-ball. 2010 Mathematics Subject Classification: 57M27, 5...

It is known that knot Floer homology detects the genus and Alexander polynomial of a knot. We investigate whether knot Floer homology of K detects more structure of minimal genus Seifert surfaces for K. We define an invariant of algebraically slice, genus one knots and provide examples to show that knot Floer homology does not detect this invariant. Finally, we remark that certain metabelian L2...

We consider combinatorial maps with fixed combinatorial knot numbered with augmenting numeration called normalized knot. We show that knot’s normalization doesn’t affect combinatorial map what concerns its generality. Knot’s normalization leads to more concise numeration of corners in maps, e.g., odd or even corners allow easy to follow distinguished cycles in map caused by the fixation of the ...