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This paper gives a connection between well chosen reductions of the Links-Gould invariants of oriented links and powers of the Alexander-Conway polynomial. We prove these formulas by showing the representations of the braid groups we derive the specialized Links-Gould polynomials from can be seen as exterior powers of copies of Burau representations.
We define a family of virtual knots generalizing the classical twist knots. We develop a recursive formula for the Alexander polynomial $Delta_0$ (as defined by Silver and Williams) of these virtual twist knots. These results are applied to provide e
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
Conway-normalized Alexander polynomial of ribbon knots depend only on their ribbon diagrams. Here ribbon diagram means a ribbon spanning the ribbon knot marked with the information of singularities. We further give an algorithm to calculate Alexander
There are many studies about twisted Alexander invariants for knots and links, but calculations of twisted Alexander invariants for spatial graphs, handlebody-knots, and surface-links have not been demonstrated well. In this paper, we give some remar