HOMFLY-PT skein module of singular links in the three-sphere

For a ring R, we denote by R[L] the free R-module spanned by the isotopy classes of singular links in S. Given two invertible elements x, t ∈ R, the HOMFLY-PT skein module of singular links in S (relative to the triple (R, t, x)) is the quotient of R[L] 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. AMS Subject Classification. Primary: 57M25.