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.

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Keywords

colored Jones polynomial, skein theory, twist knots

Mathematical Subject Classification 2000

Primary: 57M25

Secondary: 57M27

References

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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

Abstract