The skein module of torus knots complements

TL;DR

This paper computes the Kauffman skein module of torus knot complements, revealing an isomorphism to the algebra of SL(2,C)-characters combined with Laurent polynomial rings, advancing understanding of knot invariants.

Contribution

It establishes an explicit isomorphism between the skein module of torus knot complements and a well-understood algebraic structure, providing new insights into knot theory and quantum invariants.

Findings

Skein modules of torus knot complements are isomorphic to SL(2,C)-character algebras tensor Laurent polynomials

The structure of these skein modules can be explicitly described

This work links skein theory with character varieties in a new way

Abstract

We compute the Kauffman skein module of the complement of torus knots in S^3. Precisely, we show that these modules are isomorphic to the algebra of Sl(2,C)-characters tensored with the ring of Laurent polynomials.