Torus Knots and the Chern-Simons path integral: a rigorous treatment

الأصل · EN

In 1993 Rosso and Jones computed for every simple, complex Lie algebra gC and every colored torus knot in S³ the value of the corresponding Uq(gC)-quantum invariant by using the machinery of quantum groups. In the present paper we derive a S² x S¹-analogue of the Rosso-Jones formula (for colored torus ribbon knots) directly from a rigorous realization of the corresponding (gauge fixed) Chern-Simons path integral. In order to compare the explicit expressions obtained for torus knots in S² x S¹ with those for torus knots in S³ one can perform a suitable surgery operation. By doing so we verify that the original Rosso-Jones formula is indeed recovered for every gC.