{
  "id": "1712.05480",
  "version": "v1",
  "published": "2017-12-15T00:02:00.000Z",
  "updated": "2017-12-15T00:02:00.000Z",
  "title": "Higher horospherical limit sets for G-modules over CAT(0) spaces",
  "authors": [
    "Robert Bieri",
    "Ross Geoghegan"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "The Sigma-invariants of Bieri-Neumann-Strebel and Bieri-Renz involve an action of a discrete group G on a geometrically suitable space M. In the early versions, M was always a finite-dimensional Euclidean space on which G acted by translations. A substantial literature exists on this, connecting the invariants to group theory and to tropical geometry (which, actually, Sigma-theory anticipated). More recently, we have generalized these invariants to the case where M is a proper CAT(0) space on which G acts by isometries. The \"0th stage\" of this was developed in our paper [BG16]. The present paper provides a higher-dimensional extension of the theory to the \"nth stage\" for any n.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-15T00:02:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65",
      "20E42",
      "14T05"
    ],
    "keywords": [
      "higher horospherical limit sets",
      "finite-dimensional euclidean space",
      "0th stage",
      "proper cat",
      "discrete group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}