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

Hiroshi Goda; Takayuki Morifuji

doi:10.5802/ambp.416

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

Annales mathématiques Blaise Pascal, Tome 30 (2023) no. 1, pp. 75-95.

Résumé

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.

Publié le : 2023-10-26

DOI : 10.5802/ambp.416

Classification : 57K14, 57K10, 57K32
Mots clés : Twisted Alexander polynomial, chirality, hyperbolic 3-cone-manifold, twist knot

Affiliations des auteurs :

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

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {Hiroshi Goda and Takayuki Morifuji},
     title = {Twisted {Alexander} polynomials, chirality, and local deformations of hyperbolic 3-cone-manifolds},
     journal = {Annales math\'ematiques Blaise Pascal},
     pages = {75--95},
     publisher = {Universit\'e Clermont Auvergne, Laboratoire de math\'ematiques Blaise Pascal},
     volume = {30},
     number = {1},
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     doi = {10.5802/ambp.416},
     language = {en},
     url = {https://ambp.centre-mersenne.org/articles/10.5802/ambp.416/}
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Hiroshi Goda; Takayuki Morifuji. Twisted Alexander polynomials, chirality, and local deformations of hyperbolic 3-cone-manifolds. Annales mathématiques Blaise Pascal, Tome 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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