{
  "id": "2302.02510",
  "version": "v1",
  "published": "2023-02-06T00:32:33.000Z",
  "updated": "2023-02-06T00:32:33.000Z",
  "title": "Characteristic Topological Invariants",
  "authors": [
    "Oliver Knill"
  ],
  "comment": "19 pages, 1 figure",
  "categories": [
    "math.CO",
    "cs.DM"
  ],
  "abstract": "The higher characteristics w_m(G) for a finite abstract simplicial complex G are topological invariants that satisfy k-point Green function identities and can be computed in terms of Euler characteristic in the case of closed manifolds, where we give a new proof of w_m(G)=w_1(G). Also the sphere formula generalizes: for any simplicial complex, the total higher characteristics of unit spheres at even dimensional simplices is equal to the total higher characteristic of unit spheres at odd dimensional simplices.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-02-06T00:32:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M15",
      "68R10",
      "55U10"
    ],
    "keywords": [
      "characteristic topological invariants",
      "total higher characteristic",
      "satisfy k-point green function identities",
      "finite abstract simplicial complex",
      "unit spheres"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}