New York Journal of Mathematics
Volume 25 (2019), 1240-1258


Hoang-An Nguyen and Anh T. Tran

Twisted Alexander polynomials of twisted Whitehead links

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Published: November 5, 2019.
Keywords: Reidemeister torsion, twisted Alexander polynomial, twisted Whitehead link.
Subject: Primary 57M27, Secondary 57M05, 57M25.

The twisted Alexander polynomial has been explicitly computed for a few classes of knots and links, including twist knots [11] and genus one two-bridge knots [18]. In this paper we compute the two-variable twisted Alexander polynomial of twisted Whitehead links for SL2(C)-representations. As an application, we verify the hyperbolic torsion conjecture in [3,14] for twisted Whitehead links. We also obtain a formula for the Reidemeister torsion of the 3-manifold obtained from S3 by (p/l)-surgery along one component of twisted Whitehead links.


The second author has been partially supported by a grant from the Simons Foundation (#354595 to AT)

Author information

Hoang-An Nguyen:
Department of Mathematics
The University of Iowa
Iowa City, Iowa 52242, USA


Anh T. Tran:
Department of Mathematical Sciences
The University of Texas at Dallas
Richardson, TX 75080, USA