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-3. Given two invertible elements x, t is an element of R, the HOMFLY-PT skein module of singular links in S-3 (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.