{
  "id": "1901.07406",
  "version": "v1",
  "published": "2019-01-22T15:17:29.000Z",
  "updated": "2019-01-22T15:17:29.000Z",
  "title": "A parity for 2-colourable links",
  "authors": [
    "William Rushworth"
  ],
  "comment": "32 pages, 15 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "We introduce the 2-colour parity. It is a theory of parity for a large class of virtual links, defined using the interaction between orientations of the link components and a certain type of colouring. The 2-colour parity is an extension of the Gaussian parity, to which it reduces on virtual knots. We show that the 2-colour parity descends to a parity on free links. We compare the 2-colour parity to other parity theories of virtual links, focusing on a theory due to Im and Park. The 2-colour parity yields a strictly stronger invariant than the Im-Park parity. We introduce an invariant, the 2-colour writhe, that takes the form of a string of integers. The 2-colour writhe is a concordance invariant, and so obstructs sliceness. It is also an obstruction to amphichirality and chequerboard colourability within a concordance class.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-22T15:17:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M27",
      "57N70"
    ],
    "keywords": [
      "virtual links",
      "chequerboard colourability",
      "obstructs sliceness",
      "concordance invariant",
      "large class"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}