Skein-theoretical derivation of some formulas of Habiro

الأصل · EN

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.