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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.
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
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
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 $C_{n}$-
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.
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