{
  "id": "1809.06492",
  "version": "v1",
  "published": "2018-09-18T00:45:44.000Z",
  "updated": "2018-09-18T00:45:44.000Z",
  "title": "Knot Invariants from Laplacian Matrices",
  "authors": [
    "Daniel S. Silver",
    "Susan G. Williams"
  ],
  "comment": "8 pages, 8 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "A checkerboard graph of a special diagram of an oriented link is made a directed, edge-weighted graph in a natural way so that a principal minor of its Laplacian matrix is a Seifert matrix of the link. Doubling and weighting the edges of the graph produces a second Laplacian matrix such that a principal minor is an Alexander matrix of the link. The Goeritz matrix and signature invariants are obtained in a similar way. A device introduced by L. Kauffman makes it possible to apply the method to general diagrams.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-18T00:45:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M15"
    ],
    "keywords": [
      "knot invariants",
      "principal minor",
      "second laplacian matrix",
      "goeritz matrix",
      "similar way"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}