ترغب بنشر مسار تعليمي؟ اضغط هنا

Alexander and Jones polynomials of surgerized tst links

69   0   0.0 ( 0 )
 نشر من قبل Wilson Wong Yiu Shing
 تاريخ النشر 2019
  مجال البحث فيزياء
والبحث باللغة English




اسأل ChatGPT حول البحث

This paper is a continuation on the 2012 paper on Cutting Twisted Solid Tori (TSTs), in which we considered twisted solid torus links (tst links). We generalize the notion of tst links to surgerized tst links: recall that when performing $Phi^mu(n(tau), d(tau), M)$ on a tst $langle tau rangle$ where $M$ is odd, we obtain the tst link, $[Phi^mu(n(tau), d(tau), M)]$ that contains a trivial knot as one of its components. We then perform another operation $Phi^{mu}(n(tau ), d(tau ), M)$ on that trivial knot to create a new link, which we call a surgerized tst link (stst link). If $M$ is odd, we can repeat the process to give more complicated stst links. We compute braid words, Alexander and Jones polynomials of such links.



قيم البحث

اقرأ أيضاً

In this paper we give an explicit formula for the twisted Alexander polynomial of any torus link and show that it is a locally constant function on the $SL(2, mathbb C)$-character variety. We also discuss similar things for the higher dimensional twi sted Alexander polynomial and the Reidemeister torsion.
In this paper we apply the twisted Alexander polynomial to study the fibering and genus detecting problems for oriented links. In particular we generalize a conjecture of Dunfield, Friedl and Jackson on the torsion polynomial of hyperbolic knots to h yperbolic links, and confirm it for an infinite family of hyperbolic 2-bridge links. Moreover we consider a similar problem for parabolic representations of 2-bridge link groups.
83 - Ryo Nikkuni 2016
The Jones polynomial $V_{L}(t)$ for an oriented link $L$ is a one-variable Laurent polynomial link invariant discovered by Jones. For any integer $nge 3$, we show that: (1) the difference of Jones polynomials for two oriented links which are $C_{n}$- equivalent is divisible by $left(t-1right)^{n}left(t^{2}+t+1right)left(t^{2}+1right)$, and (2) there exists a pair of two oriented knots which are $C_{n}$-equivalent such that the difference of the Jones polynomials for them equals $left(t-1right)^{n}left(t^{2}+t+1right)left(t^{2}+1right)$.
We show that if a link J in the 3-sphere is homotopy ribbon concordant to a link L then the Alexander polynomial of L divides the Alexander polynomial of J.
63 - Blake Mellor 2016
We give a new interpretation of the Alexander polynomial $Delta_0$ for virtual knots due to Sawollek and Silver and Williams, and use it to show that, for any virtual knot, $Delta_0$ determines the writhe polynomial of Cheng and Gao (equivalently, Ka uffmans affine index polynomial). We also use it to define a second-order writhe polynomial, and give some applications.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا