Results 11 to 20 of about 288,674 (278)
FIBERED KNOTS AND VIRTUAL KNOTS [PDF]
Journal of Knot Theory and Its Ramifications, 2013 We introduce a new technique for studying classical knots with the methods of virtual knot theory. Let K be a knot and J be a knot in the complement of K with lk (J, K) = 0. Suppose there is covering space [Formula: see text], where V(J) is a regular neighborhood of J satisfying V(J) ∩ im (K) = ∅ and Σ is a connected compact orientable 2-manifold.
Chrisman M.W., Manturov V.O.
openaire +4 more sources
Angewandte Chemie International Edition, 2017 AbstractThe first synthetic molecular trefoil knot was prepared in the late 1980s. However, it is only in the last few years that more complex small‐molecule knot topologies have been realized through chemical synthesis. The steric restrictions imposed on molecular strands by knotting can impart significant physical and chemical properties, including ...
Fielden, SDP, Leigh, DA, Woltering, SL
openaire +4 more sources
Journal of Knot Theory and Its Ramifications, 2011 A Chebyshev knot is a knot which admits a parametrization of the form x(t) = Ta(t); y(t) = Tb(t); z(t) = Tc(t + ϕ), where a, b, c integers, Tn(t) is the Chebyshev polynomial of degree n, and φ ∈ R. Chebyshev knots are non-compact analogues of the classical Lissajous knots. We show that there are infinitely many Chebyshev knots with φ = 0.
Koseleff, Pierre-Vincent, Pecker, Daniel
openaire +2 more sources
Subknots in ideal knots, random knots and knotted proteins [PDF]
Scientific Reports, 2015 AbstractWe introduce disk matrices which encode the knotting of all subchains in circular knot configurations. The disk matrices allow us to dissect circular knots into their subknots, i.e. knot types formed by subchains of the global knot. The identification of subknots is based on the study of linear chains in which a knot type is associated to the ...
Rawdon, Eric J. +2 more
openaire +6 more sources
Knot Floer Homology of (1, 1)-Knots [PDF]
Geometriae Dedicata, 2005 17 pages, 17 ...
Goda, H., Matsuda, H., Morifuji, T.
openaire +3 more sources
Knotting trivial knots and resulting knot types [PDF]
Pacific Journal of Mathematics, 1993 Let \((V,K)\) be a pattern (i.e. \(V\) is a standardly embedded solid torus in oriented \(S^ 3\) and \(K\) a knot in \(V\)) and \(f\) an orientation preserving embedding from \(V\) into \(S^ 3\) such that \(f(V)\) is knotted. Answers to the following questions are given depending upon whether the winding number of \(K_ 2\) in \(V\) is zero or not.
openaire +2 more sources
Physical Review E, 2007 We report on the geometry and mechanics of knotted stiff strings. We discuss both closed and open knots. Our two main results are: (i) Their equilibrium energy as well as the equilibrium tension for open knots depend on the type of knot as the square of the bridge number; (ii) Braid localization is found to be a general feature of stiff strings ...
Gallotti, R., Pierre-Louis, O.
openaire +4 more sources
Structure of symmetry group of some composite links and some applications
Applied General Topology, 2020 In this paper, we study the symmetry group of a type of composite topological links, such as 22m#22 . We have done a complete analysis on the elements of the symmetric group of this link and show the structure of the group. The results can be generalized
Yang Liu
doaj +1 more source
Journal of Knot Theory and Its Ramifications, 2016 The harmonic knot [Formula: see text] is parametrized as [Formula: see text] where [Formula: see text], [Formula: see text] and [Formula: see text] are pairwise coprime integers and [Formula: see text] is the degree [Formula: see text] Chebyshev polynomial of the first kind. We classify the harmonic knots [Formula: see text] for [Formula: see text] We
Koseleff, Pierre-Vincent, Pecker, Daniel
openaire +4 more sources
Prime component-preservingly amphicheiral link with odd minimal crossing number [PDF]
, 2015 For every odd integer $c\ge 21$, we raise an example of a prime component-preservingly amphicheiral link with the minimal crossing number $c$. The link has two components, and consists of an unknot and a knot which is $(-)$-amphicheiral with odd minimal ...
Kadokami, Teruhisa, Kobatake, Yoji
core +3 more sources