{
  "id": "1206.2521",
  "version": "v1",
  "published": "2012-06-12T13:28:51.000Z",
  "updated": "2012-06-12T13:28:51.000Z",
  "title": "HOMFLY-PT skein module of singular links in the three-sphere",
  "authors": [
    "Luis Paris",
    "Emmanuel Wagner"
  ],
  "categories": [
    "math.GT"
  ],
  "abstract": "For a ring $R$, we denote by $R[\\mathcal L]$ the free $R$-module spanned by the isotopy classes of singular links in $\\mathbb S^3$. Given two invertible elements $x,t \\in R$, the HOMFLY-PT skein module of singular links in $\\mathbb S^3$ (relative to the triple $(R,t,x)$) is the quotient of $R[\\mathcal L]$ 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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-06-12T13:28:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "homfly-pt skein module",
      "singular links",
      "three-sphere",
      "conway skein module",
      "isotopy classes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1206.2521P"
    }
  }
}