#### 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.

Notes on file formats
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

Email: masbaum@math.jussieu.fr

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