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

5 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 - 2008 Nov
Externally published	Yes

Keywords

Alexander polynomial
Colored Jones polynomial
Knot
Volume conjecture

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

Access to Document

10.1142/S0219199708003034

Cite this

@article{a080c35e65b04116a249fdeed21f3bcd,

title = "Colored Jones polynomials with polynomial growth",

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.",

keywords = "Alexander polynomial, Colored Jones polynomial, Knot, Volume conjecture",

author = "Kazuhiro Hikami and Hitoshi Murakami",

year = "2008",

month = nov,

doi = "10.1142/S0219199708003034",

language = "English",

volume = "10",

pages = "815--834",

journal = "Communications in Contemporary Mathematics",

issn = "0219-1997",

publisher = "World Scientific Publishing Co. Pte Ltd",

number = "SUPPL. 1",

}

TY - JOUR

T1 - Colored Jones polynomials with polynomial growth

AU - Hikami, Kazuhiro

AU - Murakami, Hitoshi

PY - 2008/11

Y1 - 2008/11

N2 - 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.

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.

KW - Alexander polynomial

KW - Colored Jones polynomial

KW - Knot

KW - Volume conjecture

UR - http://www.scopus.com/inward/record.url?scp=56749132480&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=56749132480&partnerID=8YFLogxK

U2 - 10.1142/S0219199708003034

DO - 10.1142/S0219199708003034

M3 - Article

AN - SCOPUS:56749132480

SN - 0219-1997

VL - 10

SP - 815

EP - 834

JO - Communications in Contemporary Mathematics

JF - Communications in Contemporary Mathematics

IS - SUPPL. 1

ER -

Colored Jones polynomials with polynomial growth

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this