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December 2018 From Colored Jones Invariants to Logarithmic Invariants
Jun MURAKAMI
Tokyo J. Math. 41(2): 453-475 (December 2018). DOI: 10.3836/tjm/1502179244

Abstract

In this paper, we express the logarithmic invariant of knots in terms of derivatives of the colored Jones invariants. Logarithmic invariant is defined by using the Jacobson radicals of the restricted quantum group $\overline{\mathcal U}_\xi(sl_2)$ where $\xi$ is a root of unity. We also propose a version of the volume conjecture stating a relation between the logarithmic invariants and the hyperbolic volumes of the cone manifolds along a knot, which is proved for the figure-eight knot.

Citation

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Jun MURAKAMI. "From Colored Jones Invariants to Logarithmic Invariants." Tokyo J. Math. 41 (2) 453 - 475, December 2018. https://doi.org/10.3836/tjm/1502179244

Information

Published: December 2018
First available in Project Euclid: 20 November 2017

zbMATH: 07053486
MathSciNet: MR3908804
Digital Object Identifier: 10.3836/tjm/1502179244

Subjects:
Primary: 57M27
Secondary: 17B37, 51M25

Rights: Copyright © 2018 Publication Committee for the Tokyo Journal of Mathematics

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Vol.41 • No. 2 • December 2018
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