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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 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 2000
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