اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدThe Kauffman bracket ideal for genus-1 tangles
150
0
0.0
(
0
)
تأليف
Susan M. Abernathy
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Given a compact oriented 3-manifold M in S^3 with boundary, an (M,2n)-tangle T is a 1-manifold with 2n boundary components properly embedded in M. We say that T embeds in a link L in S^3 if T can be completed to L by a 1-manifold with 2n boundary components exterior to M. The link L is called a closure of T. We define the Kauffman bracket ideal of T to be the ideal I_T generated by the reduced Kauffman bracket polynomials of all closures of T. If this ideal is non-trivial, then T does not embed in the unknot. We give an algorithm for computing a finite list of generators for the Kauffman bracket ideal of any (S^1 x D^2, 2)-tangle, also called a genus-1 tangle, and give an example of a genus-1 tangle with non-trivial Kauffman bracket ideal. Furthermore, we show that if a single-component genus-1 tangle S can be obtained as the partial closure of a (B^3, 4)-tangle T, then I_T = I_S.
قيم البحث
اقرأ أيضاً
This paper refines previous work by the first author. We study the question of which links in the 3-sphere can be obtained as closures of a given 1-manifold in an unknotted solid torus in the 3-sphere (or genus-1 tangle) by adjoining another 1-manifo
ld in the complementary solid torus. We distinguish between even and odd closures, and define even and o
This paper bounds the computational cost of computing the Kauffman bracket of a link in terms of the crossing number of that link. Specifically, it is shown that the image of a tangle with $g$ boundary points and $n$ crossings in the Kauffman bracket
skein module is a linear combination of $O(2^g)$ basis elements, with each coefficient a polynomial with at most $n$ nonzero terms, each with integer coefficients, and that the link can be built one crossing at a time as a sequence of tangles with maximum number of boundary points bounded by $Csqrt{n}$ for some $C.$ From this it follows that the computation of the Kauffman bracket of the link takes time and memory a polynomial in $n$ times $2^{Csqrt{n}}.$
We define stable homotopy refinements of Khovanovs arc algebras and tangle invariants.
We use Kauffmans bracket polynomial to define a complex-valued invariant of virtual rational tangles that generalizes the well-known fraction invariant for classical rational tangles. We provide a recursive formula for computing the invariant, and use it to compute several examples.
Biquandle brackets define invariants of classical and virtual knots and links using skein invariants of biquandle-colored knots and links. Biquandle coloring quivers categorify the biquandle counting invariant in the sense of defining quiver-valued e
nhancements which decategorify to the counting invariant. In this paper we unite the two ideas to define biquandle bracket quivers, providing new categorifications of biquandle brackets. In particular, our construction provides an infinite family of categorifications of the Jones polynomial and other classical skein invariants.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
