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arXiv · 2609.36772

Quantitative finiteness of monic characters of knots

Taehee Kim·Takayuki Morifuji
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Abstract

Dunfield, Friedl, and Jackson showed that if the $SL(2, \mathbb{C})$-character variety of a knot has an irreducible curve component that contains the character of an irreducible representation and a character with nonmonic twisted Alexander polynomial, then this component has only finitely many characters with monic twisted Alexander polynomials. In this paper, we give explicit upper bounds on the number of such characters in terms of a presentation of the knot group. In particular, we give upper bounds in terms of the crossing number of the knot.

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Taehee Kim, Takayuki Morifuji. 2026-09-29. Quantitative finiteness of monic characters of knots. https://arxiv.org/abs/2609.36772

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