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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 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.

preprint2003arXivOpen access
Gregor Masbaum
math.QAmath.GT
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Gregor Masbaum

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