This paper resolves the problem of comparing the skein modules defined using the skein relations discovered by Melvin and Kirby that underlie the quantum group-based Reshetikhin–Turaev model for [Formula: see text] Chern–Simons theory to the Kauffman bracket skein modules. Several applications and examples are presented.

This paper resolves the problem of comparing the skein modules defined using the skein relations discovered by P. Melvin and R. Kirby that underlie the Reshetikhin-Turaev model for SU (2) Chern-Simons theory to the Kauffman bracket skein modules. Several applications and examples are presented.