2015/08/16 by Hahn, Atle
#57M27 #81T08 #81T45 #FOS: Physical sciences #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.1508.03804
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.