Algebraic and Geometric Topology 3 (2003), paper no. 17, pages 537-556.

Skein-theoretical derivation of some formulas of Habiro

Gregor Masbaum

Abstract. We use skein theory to compute the coefficients of certain power series considered by Habiro in his theory of sl_2 invariants of integral homology 3-spheres. Habiro originally derived these formulas using the quantum group U_q sl_2. As an application, we give a formula for the colored Jones polynomial of twist knots, generalizing formulas of Habiro and Le for the trefoil and the figure eight knot.

Keywords. Colored Jones polynomial, skein theory, twist knots

AMS subject classification. Primary: 57M25. Secondary: 57M27.

DOI: 10.2140/agt.2003.3.537

E-print: arXiv:math.GT/0306345

Submitted: 12 December 2002. Accepted: 22 May 2003. Published: 16 June 2003.

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Gregor Masbaum
Institut de Mathematiques de Jussieu (UMR 7586 du CNRS)
Universite Paris 7 (Denis Diderot), Case 7012
2, place Jussieu, 75251 Paris Cedex 05, France

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