{
  "id": "2006.13793",
  "version": "v1",
  "published": "2020-06-24T15:06:55.000Z",
  "updated": "2020-06-24T15:06:55.000Z",
  "title": "Decomposition of Pointwise Finite-Dimensional S^1 Persistence Modules",
  "authors": [
    "Eric J. Hanson",
    "Job D. Rock"
  ],
  "comment": "15 pages, 2 figures, comments welcome!",
  "categories": [
    "math.RT",
    "math.AT"
  ],
  "abstract": "We prove that pointwise finite-dimensional S^1 persistence modules over an arbitrary field decompose uniquely, up to isomorphism, into the direct sum of a bar code and finitely-many Jordan cells. These persistence modules have also been called angle-valued or circular persistence modules. We also show that a pointwise finite-dimensional S^1 persistence module is indecomposable if and only if it is a bar or Jordan cell (a string or a band module, respectively, in the language of representation theory).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-24T15:06:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G20",
      "55N31"
    ],
    "keywords": [
      "pointwise finite-dimensional",
      "decomposition",
      "circular persistence modules",
      "finitely-many jordan cells",
      "arbitrary field decompose"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}