Colored Jones polynomials with polynomial growth

Kazuhiro Hikami; Hitoshi Murakami

doi:10.1142/S0219199708003034

Colored Jones polynomials with polynomial growth

Kazuhiro Hikami, Hitoshi Murakami

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

6 Citations (Scopus)

Abstract

The volume conjecture and its generalizations say that the colored Jones polynomial corresponding to the N-dimensional irreducible representation of sl(2;ℂ) of a (hyperbolic) knot evaluated at exp(c/N) grows exponentially with respect to N if one fixes a complex number c near 2 π √-1. On the other hand if the absolute value of c is small enough, it converges to the inverse of the Alexander polynomial evaluated at exp c. In this paper we study cases where it grows polynomially.

Original language	English
Pages (from-to)	815-834
Number of pages	20
Journal	Communications in Contemporary Mathematics
Volume	10
Issue number	SUPPL. 1
DOIs	https://doi.org/10.1142/S0219199708003034
Publication status	Published - Nov 2008
Externally published	Yes

All Science Journal Classification (ASJC) codes

Mathematics(all)
Applied Mathematics

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abstract = "The volume conjecture and its generalizations say that the colored Jones polynomial corresponding to the N-dimensional irreducible representation of sl(2;ℂ) of a (hyperbolic) knot evaluated at exp(c/N) grows exponentially with respect to N if one fixes a complex number c near 2 π √-1. On the other hand if the absolute value of c is small enough, it converges to the inverse of the Alexander polynomial evaluated at exp c. In this paper we study cases where it grows polynomially.",

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AB - The volume conjecture and its generalizations say that the colored Jones polynomial corresponding to the N-dimensional irreducible representation of sl(2;ℂ) of a (hyperbolic) knot evaluated at exp(c/N) grows exponentially with respect to N if one fixes a complex number c near 2 π √-1. On the other hand if the absolute value of c is small enough, it converges to the inverse of the Alexander polynomial evaluated at exp c. In this paper we study cases where it grows polynomially.

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Colored Jones polynomials with polynomial growth

Abstract

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