The colored Jones polynomial and the A-polynomial of Knots

• Autores: Thang T.Q. Lê
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 207, Nº 2, 2006, págs. 782-804
• Idioma: inglés
• DOI: 10.1016/j.aim.2006.01.006
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• Resumen

  • We study relationships between the colored Jones polynomial and the A-polynomial of a knot. The AJ conjecture (of Garoufalidis) that relates the colored Jones polynomial and the A-polynomial is established for a large class of two-bridge knots, including all twist knots. We formulate a weaker conjecture and prove that it holds for all two-bridge knots. Along the way we also calculate the Kauffman bracket skein module of the complements of two-bridge knots. Some properties of the colored Jones polynomial are established.