A version of the volume conjecture

Hitoshi Murakami

doi:10.1016/j.aim.2006.09.005

A version of the volume conjecture

Hitoshi Murakami

INF - Computer and Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

We propose a version of the volume conjecture that would relate a certain limit of the colored Jones polynomials of a knot to the volume function defined by a representation of the fundamental group of the knot complement to the special linear group of degree two over complex numbers. We also confirm the conjecture for the figure-eight knot and torus knots. This version is different from S. Gukov's because of a choice of polarization.

Original language	English
Pages (from-to)	678-683
Number of pages	6
Journal	Advances in Mathematics
Volume	211
Issue number	2
DOIs	https://doi.org/10.1016/j.aim.2006.09.005
Publication status	Published - 2007 Jun 1

Keywords

A-Polynomial
Alexander polynomial
Colored Jones polynomial
Figure-eight knot
Torus knot
Volume conjecture

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10.1016/j.aim.2006.09.005

Cite this

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AB - We propose a version of the volume conjecture that would relate a certain limit of the colored Jones polynomials of a knot to the volume function defined by a representation of the fundamental group of the knot complement to the special linear group of degree two over complex numbers. We also confirm the conjecture for the figure-eight knot and torus knots. This version is different from S. Gukov's because of a choice of polarization.

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KW - Alexander polynomial

KW - Colored Jones polynomial

KW - Figure-eight knot

KW - Torus knot

KW - Volume conjecture

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JO - Advances in Mathematics

JF - Advances in Mathematics

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ER -

A version of the volume conjecture

Abstract

Keywords

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