#### Volume 3, issue 1 (2003)

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Skein-theoretical derivation of some formulas of Habiro

### Gregor Masbaum

Algebraic & Geometric Topology 3 (2003) 537–556
 arXiv: math.GT/0306345
##### Abstract

We use skein theory to compute the coefficients of certain power series considered by Habiro in his theory of ${\mathfrak{s}\mathfrak{l}}_{2}$ invariants of integral homology $3$–spheres. Habiro originally derived these formulas using the quantum group ${U}_{q}{\mathfrak{s}\mathfrak{l}}_{2}$. 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
Primary: 57M25
Secondary: 57M27
##### Publication
Received: 12 December 2002
Accepted: 22 May 2003
Published: 16 June 2003
##### Authors
 Gregor Masbaum Institut de Mathématiques de Jussieu UMR 7586 du CNRS Université Paris 7 (Denis Diderot) Case 7012 2, place Jussieu 75251 Paris Cedex 05 France