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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747

Skein-theoretical derivation of some formulas of Habiro

Gregor Masbaum

Algebraic & Geometric Topology 3 (2003) 537–556

DOI: 10.2140/agt.2003.3.537

arXiv: math.GT/0306345

Abstract

We use skein theory to compute the coefficients of certain power series considered by Habiro in his theory of sl2 invariants of integral homology 3–spheres. Habiro originally derived these formulas using the quantum group Uqsl2. 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

Primary: 57M25

Secondary: 57M27

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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