The noncommutative A-ideal of a (2, 2p + 1)-torus knot determines its Jones polynomial

Rǎzvan Gelca, Jeremy Sain

Research output: Contribution to journalArticle

35 Scopus citations

Abstract

The noncommutative A-ideal of a knot is a generalization of the A-polynomial, defined using Kauffman bracket skein modules. In this paper we show that any knot that has the same noncommutative A-ideal as the (2, 2p+1)-torus knot has the same colored Jones polynomials. This is a consequence of the orthogonality relation, which yields a recursive relation for computing all colored Jones polynomials of the knot.

Original languageEnglish
Pages (from-to)187-201
Number of pages15
JournalJournal of Knot Theory and its Ramifications
Volume12
Issue number2
DOIs
StatePublished - Mar 2003

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