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On the 3D-index of finite cyclic covers of hyperbolic knot complements

OHTSUKI, Tomotada 京都大学

2023.05

概要

The 3D-index is an invariant of a 3-manifold with cusps, which would be related to the volume conjecture, and it would be useful to study properties of this invariant. In this paper, we calculate the 3D-index of the nth cyclic covers of hyperbolic knot complements, and show that the dth coefficient of this 3D-index is equal to a polynomial in n of degree ≤ 2d for any sufficiently large n. In particular, we calculate these polynomials concretely for lower degrees for the 4₁, 5₂, 6₁ knots.

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Research Institute for Mathematical Sciences, Kyoto University, Sakyo-ku, Kyoto, 606-8502, Japan

E-mail address: tomotada@kurims.kyoto-u.ac.jp

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