On the kashaev invariant and the twisted reidemeister torsion of two-bridge knots

Tomotada Ohtsuki, Toshie Takata

研究成果: ジャーナルへの寄稿記事

9 引用 (Scopus)

抄録

It is conjectured that, in the asymptotic expansion of the Kashaev invariant of a hyperbolic knot, the first coefficient is represented by the complex volume of the knot complement, and the second coefficient is represented by a constant multiple of the square root of the twisted Reidemeister torsion associated with the holonomy representation of the hyperbolic structure of the knot complement. In particular, this conjecture has been rigorously proved for some simple hyperbolic knots, for which the second coefficient is presented by a modification of the square root of the Hessian of the potential function of the hyperbolic structure of the knot complement. In this paper, we define an invariant of a parametrized knot diagram as a modification of the Hessian of the potential function obtained from the parametrized knot diagram. Further, we show that this invariant is equal (up to sign) to a constant multiple of the twisted Reidemeister torsion for any two-bridge knot.

元の言語英語
ページ(範囲)853-952
ページ数100
ジャーナルGeometry and Topology
19
発行部数2
DOI
出版物ステータス出版済み - 4 10 2015

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Reidemeister Torsion
Knot
Invariant
Hyperbolic Knot
Hyperbolic Structure
Complement
Potential Function
Square root
Diagram
Coefficient
Holonomy
Asymptotic Expansion

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

これを引用

On the kashaev invariant and the twisted reidemeister torsion of two-bridge knots. / Ohtsuki, Tomotada; Takata, Toshie.

:: Geometry and Topology, 巻 19, 番号 2, 10.04.2015, p. 853-952.

研究成果: ジャーナルへの寄稿記事

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