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Twisted Alexander polynomials with the adjoint action for some classes of knots

Anh T. Tran

Department of Mathematical Sciences, The University of Texas at Dallas, Richardson, TX 75080, USA

https://doi.org/10.1142/S0218216514500515Cited by:6 (Source: Crossref)

Abstract

We calculate the twisted Alexander polynomial with the adjoint action for torus knots and twist knots. As consequences of these calculations, we obtain the formula for the nonabelian Reidemeister torsion of torus knots in [J. Dubois, Nonabelian twisted Reidemeister torsion for fibered knots, Canad. Math. Bull.49(1) (2006) 55–71] and a formula for the nonabelian Reidemeister torsion of twist knots that is better than the one in [J. Dubois, V. Huynh and Y. Yamaguchi, Nonabelian Reidemeister torsion for twist knots, J. Knot Theory Ramifications18(3) (2009) 303–341].

Keywords:

AMSC: 57M27

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