Skein-theoretical derivation of some formulas of Habiro
Gregor Masbaum
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 Uq sl2. 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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