{
  "id": "1911.12698",
  "version": "v1",
  "published": "2019-11-28T13:30:03.000Z",
  "updated": "2019-11-28T13:30:03.000Z",
  "title": "Conley-Morse-Forman theory for generalized combinatorial multivector fields on finite topological spaces",
  "authors": [
    "Michał Lipiński",
    "Jacek Kubica",
    "Marian Mrozek",
    "Thomas Wanner"
  ],
  "categories": [
    "math.DS",
    "math.AT",
    "math.CO"
  ],
  "abstract": "In this paper we present the theory of combinatorial multivector fields in finite topological spaces. It generalizes the analogous theory for Lefschetz complexes recently introduced in \\cite{Mr2017}. We drop the restrictive assumpion in \\cite{Mr2017} that every multivector has a unique maximal element. In this setting we define isolated invariant sets, isolating neighborhood and index pairs and we construct the Conley index. We prove its additivity property.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-11-28T13:30:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "generalized combinatorial multivector fields",
      "finite topological spaces",
      "conley-morse-forman theory",
      "unique maximal element",
      "define isolated invariant sets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}