اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدComputing Chebyshev knot diagrams
520
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
A Chebyshev curve C(a,b,c,phi) has a parametrization of the form x(t)=Ta(t); y(t)=T_b(t) ; z(t)= Tc(t + phi), where a,b,c are integers, Tn(t) is the Chebyshev polynomial of degree n and phi in RR. When C(a,b,c,phi) has no double points, it defines a polynomial knot. We determine all possible knots when a, b and c are given.
قيم البحث
اقرأ أيضاً
We show that every two-bridge knot $K$ of crossing number $N$ admits a polynomial parametrization $x=T_3(t), y = T_b(t), z =C(t)$ where $T_k(t)$ are the Chebyshev polynomials and $b+deg C = 3N$. If $C (t)= T_c(t)$ is a Chebyshev polynomial, we call s
uch a knot a harmonic knot. We give the classification of harmonic knots for $a le 3.$ Most results are derived from continued fractions and their matrix representations.
We show that a small tree-decomposition of a knot diagram induces a small sphere-decomposition of the corresponding knot. This, in turn, implies that the knot admits a small essential planar meridional surface or a small bridge sphere. We use this to
give the first examples of knots where any diagram has high tree-width. This answers a question of Burton and of Makowsky and Mari~no.
In this article we discuss applications of neural networks to recognising knots and, in particular, to the unknotting problem. One of motivations for this study is to understand how neural networks work on the example of a problem for which rigorous
mathematical algorithms for its solution are known. We represent knots by rectangular Dynnikov diagrams and apply neural networks to distinguish a given diagram class from the given finite families of topological types. The data presented to the program is generated by applying Dynnikov moves to initial samples. The significance of using these diagrams and moves is that in this context the problem of determining whether a diagram is unknotted is a finite search of a bounded combinatorial space.
In the present paper, we consider local moves on classical and welded diagrams: (self-)crossing change, (self-)virtualization, virtual conjugation, Delta, fused, band-pass and welded band-pass moves. Interrelationship between these moves is discussed
and, for each of these move, we provide an algebraic classification. We address the question of relevant welded extensions for classical moves in the sense that the classical quotient of classical object embeds into the welded quotient of welded objects. As a by-product, we obtain that all of the above local moves are unknotting operations for welded (long) knots. We also mention some topological interpretations for these combinatorial quotients.
We re-derive Manolescus unoriented skein exact triangle for knot Floer homology over F_2 combinatorially using grid diagrams, and extend it to the case with Z coefficients by sign refinements. Iteration of the triangle gives a cube of resolutions tha
t converges to the knot Floer homology of an oriented link. Finally, we re-establish the homological sigma-thinness of quasi-alternating links.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
