The skein theory associated to the HOMFLY polynomial invariant of oriented knots and links in the three-sphere is explored in order to provide the background results necessary for the creation of a Topological Quantum Field Theory. A simple local duality result in the skein theory is proved. It allows vector space dimensions in the theory to be correlated with the structure constants in a skein algebra associated to the solid torus.
Cite this article
W.B R. Lickorish, Skeins, SU(N) three-manifold invariants and TQFT. Comment. Math. Helv. 75 (2000), no. 1, pp. 45–64DOI 10.1007/S000140050112