{
  "id": "1803.03086",
  "version": "v1",
  "published": "2018-03-08T13:43:04.000Z",
  "updated": "2018-03-08T13:43:04.000Z",
  "title": "Topological Degree of Shift Spaces on Groups",
  "authors": [
    "Jung-Chao Ban",
    "Chih-Hung Chang"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "This paper considers the topological degree of $G$-shifts of finite type for the case where $G$ is a nonabelian group. Whenever the Cayley graph of $G$ has a finite representation and the relationships among the generators of $G$ are determined by a matrix $A$, the coefficients of the characteristic polynomial of $A$ are revealed as the number of children of the graph. After introducing an algorithm for the computation of the degree, the degree spectrum, which is finite, relates to a collection of matrices in which the sum of each row of every matrix is bounded by the number of children of the graph. Furthermore, the algorithm extends to $G$ of finite followers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-03-08T13:43:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "topological degree",
      "shift spaces",
      "cayley graph",
      "nonabelian group",
      "finite type"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}