Skein-theoretical derivation of some formulas of Habiro

We use skein theory to compute the coefficients of certain power series considered by Habiro in his theory of ${s l}_{2}$ invariants of integral homology $3$ –spheres. Habiro originally derived these formulas using the quantum group $U_{q} {s l}_{2}$ . 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

Mathematical Subject Classification 2000

Primary: 57M25

Secondary: 57M27

References

Forward citations

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

Volume 3, issue 1 (2003)

Gregor Masbaum