arXiv subjects

Anh T. Tran

Publications and source records attributed to Anh T. Tran.

58 records · Page 4Linked to original sources

arXiv2013

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

For a knot $K$ in $S^3$, the $sl_2$-colored Jones function $J_K(n)$ is a sequence of Laurent polynomials in the variable $t$, which is known to satisfy non-trivial linear recurrence relations. The operator corresponding to the minimal linear recurrence relation is called the recurrence polynomial of $K$. The AJ conjecture \cite{Ga04} states that when reducing $t=-1$, the recurrence polynomial is essentially equal to the $A$-polynomial of $K$. In this paper we consider a stronger version of the AJ conjecture, proposed by Sikora \cite{Si}, and confirm it for all torus knots.

math.GT↗

arXiv2013

On left-orderable fundamental groups and Dehn surgeries on twist knots

We show that the resulting manifold by $r$-surgery on the hyperbolic twist knot $K_m, \, m \ge 2$, has left-orderable fundamental group if the slope $r$ satisfies the condition $r \in (-4,2m)$ if $m$ is even, and $r \in [0,4] \cup (\frac{4m}ω+4, 2m+4)$ if $m$ is odd, where $ω>1$ is the unique real solution of the equation $x e^{x}=4m$.

math.GT↗

arXiv2012

The Kauffman bracket skein module of two-bridge links

We calculate the Kauffman bracket skein module (KBSM) of the complement of all two-bridge links. For a two-bridge link, we show that the KBSM of its complement is free over the ring $\BC[t^{\pm 1}]$ and when reducing $t=-1$, it is isomorphic to the ring of regular functions on the character variety of the link group.

math.GT↗

arXiv2009

On the Volume Conjecture for Cables of Knots

We establish the volume conjecture for (m,2)-cables of the figure 8 knot, when m is odd. For (m,2)-cables of general knots where m is even, we show that the limit in the volume conjecture depends on the parity of the color (of the Kashaev invariant). There are many cases when the volume conjecture for cables of the figure 8 knot is false if one considers all the colors, but holds true if one restricts the colors to a subset of the set of positive integers.

math.GT↗