{
  "id": "1310.3030",
  "version": "v1",
  "published": "2013-10-11T06:36:50.000Z",
  "updated": "2013-10-11T06:36:50.000Z",
  "title": "Cocycle invariants of codimension 2-embeddings of manifolds",
  "authors": [
    "Jozef H. Przytycki",
    "Witold Rosicki"
  ],
  "comment": "47 pages, 22 figures, Proceedings of Knots in Poland III, 2010",
  "categories": [
    "math.GT"
  ],
  "abstract": "We consider the classical problem of a position of n-dimensional manifold M in R^{n+2}. We show that we can define the fundamental (n+1)-cycle and the shadow fundamental (n+2)-cycle for a fundamental quandle of a knotting M to R^{n+2}. In particular, we show that for any fixed quandle, quandle coloring, and shadow quandle coloring, of a diagram of M embedded in R^{n+2} we have (n+1)- and (n+2)-(co)cycle invariants (i.e. invariant under Roseman moves). We speculate on a similar construction for general Yang-Baxter operators.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-10-11T06:36:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57Q45",
      "57M25"
    ],
    "keywords": [
      "cocycle invariants",
      "codimension",
      "general yang-baxter operators",
      "roseman moves",
      "shadow fundamental"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 47,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.3030P"
    }
  }
}