Anh T. Tran

Twisted Alexander polynomials of 2-bridge knots for parabolic representations

In this paper we show that the twisted Alexander polynomial associated to a parabolic representation determines fiberedness and genus of a wide class of 2-bridge knots. As a corollary we give an affirmative answer to a conjecture of Dunfield, Friedl and Jackson for infinitely many hyperbolic knots.

Proof of a stronger version of the AJ Conjecture for torus knots

For a knot

The Kauffman bracket skein module of two-bridge links

K

THE UNIVERSAL CHARACTER RING OF THE (-2, 2m + 1, 2n)-PRETZEL LINK

in

The universal character ring of some families of one-relator groups

S^3

The strong AJ conjecture for cables of torus knots

, the

ON THE VOLUME CONJECTURE FOR CABLES OF KNOTS

sl_2

ON THE TWISTED ALEXANDER POLYNOMIAL FOR REPRESENTATIONS INTO SL2(ℂ)

-colored Jones function

Character varieties of (−2,2m + 1,2n)-pretzel links and twisted Whitehead links

J_K(n)

Character varieties of double twist links

is a sequence of Laurent polynomials in the variable