Colored Jones polynomials with polynomial growth

Kazuhiro Hikami, Hitoshi Murakami

Research output: Contribution to journalArticlepeer-review

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 - 2008 Nov 1
Externally publishedYes

Keywords

  • Alexander polynomial
  • Colored Jones polynomial
  • Knot
  • Volume conjecture

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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