Adjoint twisted Alexander polynomials of genus one two-bridge knots

Tran, Anh T.

doi:10.1142/s0218216516500656

Cited by 6 publications

(2 citation statements)

References 21 publications

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“…The formulas of the twisted Alexander polynomials for 2-and 3-dimensional representations are provided by Tran in [31,32]. (1) The twisted Alexander polynomial of 𝐾 associated with 𝜌 is…”

Section: Genus One Two-bridge Knotmentioning

confidence: 99%

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Twisted Alexander polynomials, chirality, and local deformations of hyperbolic 3-cone-manifolds

Goda,

Morifuji

2023

Annales Mathématiques Blaise Pascal

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In this paper, we discuss a relationship between the chirality of knots and higher-dimensional twisted Alexander polynomials associated with holonomy representations of hyperbolic 3-cone-manifolds. In particular, we provide a new necessary condition for a knot, that appears in a hyperbolic 3-cone-manifold of finite volume as a singular set, to be amphicheiral. Moreover, we can detect the chirality of hyperbolic twist knots, according to our criterion, using low-dimensional irreducible representations.

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Section: Genus One Two-bridge Knotmentioning

confidence: 99%

“…Theorem 1],[31, Theorem 1.1] ). Suppose 𝜌 : 𝐺 (𝐾) → SL(2, C) is an irreducible representation of a genus one two-bridge knot 𝐾 = 𝐽 (2𝑚, 2𝑛).…”

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confidence: 99%

Twisted Alexander polynomials, chirality, and local deformations of hyperbolic 3-cone-manifolds

Goda,

Morifuji

2023

Annales Mathématiques Blaise Pascal

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Adjoint twisted Alexander polynomial of twisted Whitehead links

Nguyen

Tran

2018

J. Knot Theory Ramifications

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The adjoint twisted Alexander polynomial has been computed for twist knots [A. Tran, Twisted Alexander polynomials with the adjoint action for some classes of knots, J. Knot Theory Ramifications 23(10) (2014) 1450051], genus one two-bridge knots [A. Tran, Adjoint twisted Alexander polynomials of genus one two-bridge knots, J. Knot Theory Ramifications 25(10) (2016) 1650065] and the Whitehead link [J. Dubois and Y. Yamaguchi, Twisted Alexander invariant and nonabelian Reidemeister torsion for hyperbolic three dimensional manifolds with cusps, Preprint (2009), arXiv:0906.1500 ]. In this paper, we compute the adjoint twisted Alexander polynomial and nonabelian Reidemeister torsion of twisted Whitehead links.

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On adjoint torsion polynomial of genus one two-bridge knots

Morifuji

2022

Kodai Math. J.

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Adjoint twisted Alexander polynomials of genus one two-bridge knots

Abstract: Abstract. We give explicit formulas for the adjoint twisted Alexander polynomial and the nonabelian Reidemeister torsion of genus one two-bridge knots.

Cited by 6 publications

References 21 publications

Twisted Alexander polynomials, chirality, and local deformations of hyperbolic 3-cone-manifolds

Twisted Alexander polynomials, chirality, and local deformations of hyperbolic 3-cone-manifolds

Adjoint twisted Alexander polynomial of twisted Whitehead links

On adjoint torsion polynomial of genus one two-bridge knots

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