Twisted Alexander polynomials, chirality, and local deformations of hyperbolic 3-cone-manifolds
Annales mathématiques Blaise Pascal, Volume 30 (2023) no. 1, pp. 75-95.

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.

Published online:
DOI: 10.5802/ambp.416
Classification: 57K14, 57K10, 57K32
Keywords: Twisted Alexander polynomial, chirality, hyperbolic 3-cone-manifold, twist knot
Hiroshi Goda 1; Takayuki Morifuji 2

1 Department of Mathematics Tokyo University of Agriculture and Technology 2-24-16 Naka-cho, Koganei, Tokyo 184-8588 JAPAN
2 Department of Mathematics, Hiyoshi Campus Keio University Yokohama 223-8521 JAPAN
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Hiroshi Goda; Takayuki Morifuji. Twisted Alexander polynomials, chirality, and local deformations of hyperbolic 3-cone-manifolds. Annales mathématiques Blaise Pascal, Volume 30 (2023) no. 1, pp. 75-95. doi : 10.5802/ambp.416. https://ambp.centre-mersenne.org/articles/10.5802/ambp.416/

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