Colored Jones polynomials with polynomial growth

Kazuhiro Hikami, Hitoshi Murakami

Research output: Contribution to journalArticle

4 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 languageEnglish
Pages (from-to)815-834
Number of pages20
JournalCommunications in Contemporary Mathematics
Volume10
Issue numberSUPPL. 1
DOIs
Publication statusPublished - Nov 1 2008
Externally publishedYes

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Colored Jones Polynomial
Hyperbolic Knot
Alexander Polynomial
Polynomial Growth
Complex number
Absolute value
Irreducible Representation
Polynomials
Converge
Generalization

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Cite this

Colored Jones polynomials with polynomial growth. / Hikami, Kazuhiro; Murakami, Hitoshi.

In: Communications in Contemporary Mathematics, Vol. 10, No. SUPPL. 1, 01.11.2008, p. 815-834.

Research output: Contribution to journalArticle

Hikami, Kazuhiro ; Murakami, Hitoshi. / Colored Jones polynomials with polynomial growth. In: Communications in Contemporary Mathematics. 2008 ; Vol. 10, No. SUPPL. 1. pp. 815-834.
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