HOMFLY-PT SKEIN MODULE OF SINGULAR LINKS IN THE THREE-SPHERE

Abstract

For a ring R, we denote by [Formula: see text] the free R-module spanned by the isotopy classes of singular links in 𝕊3. Given two invertible elements x, t ∈ R, the HOMFLY-PT skein module of singular links in 𝕊3 (relative to the triple (R, t, x)) is the quotient of [Formula: see text] by local relations, called skein relations, that involve t and x. We compute the HOMFLY-PT skein module of singular links for any R such that (t-1 - t + x) and (t-1 - t - x) are invertible. In particular, we deduce the Conway skein module of singular links.