Tran, Anh T.
Anh Tran is an Associate Professor of Mathematics. His research interests are focused on quantum topology and knot theory especially as they relate to the Jones polynomial, skein modules, charactyer varieties, the A-polynomial, the Alexander polynomial, and left-orderability of fundamental groups.
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(Japan Academy, 2019-01)We show that the fundamental group of the 3-manifold obtained by p/q-surgery along the (n - 2)-twisted (3, 3m + 2)-torus knot, with n, m ≥ 1, is not left-orderable if p/q ≥ 2n + 6m - 3 and is left-orderable if p/q is ...
The Asymptotics of the Higher Dimensional Reidemeister Torsion for Exceptional Surgeries Along Twist Knots We determine the asymptotic behavior of the higher dimensional Reidemeister torsion for the graph manifolds obtained by exceptional surgeries along twist knots. We show that all irreducible SL2
(2015-07-07)We confirm the AJ conjecture [Ga2] that relates the A-polynomial and the colored Jones polynomial for hyperbolic knots satisfying certain conditions. In particular, we show that the conjecture holds true for some classes ...
(University at Albany, 2015-09-16)We study the behavior of the degree of the colored Jones polynomial and the boundary slopes of knots under the operation of cabling. We show that, under certain hypothesis on this degree, if a knot K satisfies the Slope ...