Skein-theoretical derivation of some formulas of Habiro

Details Skein-theoretical derivation of some formulas of Habiro Skein-theoretical derivation of some formulas of Habiro

2003-06-24

arxiv.org/abs/math/0306345v1

Algebr. Geom. Topol. 3 (2003) 537-556

Mathematics

Geometric Topology

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-17.abs.html

Scientific paper

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.

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