{
  "id": "2107.04574",
  "version": "v1",
  "published": "2021-07-09T17:47:04.000Z",
  "updated": "2021-07-09T17:47:04.000Z",
  "title": "Configuration spaces of disks in a strip, twisted algebras, persistence, and other stories",
  "authors": [
    "Hannah Alpert",
    "Fedor Manin"
  ],
  "comment": "45 pages, 15 figures. Builds on and supersedes arXiv:2006.01240",
  "categories": [
    "math.AT",
    "math.CO",
    "math.RT"
  ],
  "abstract": "We give $\\mathbb{Z}$-bases for the homology and cohomology of the configuration space $\\operatorname{config}(n,w)$ of $n$ unit disks in an infinite strip of width $w$, first studied by Alpert, Kahle and MacPherson. We also study the way these spaces evolve both as $n$ increases (using the framework of representation stability) and as $w$ increases (using the framework of persistent homology). Finally, we include some results about the cup product in the cohomology and about the configuration space of unordered disks.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-09T17:47:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55R80",
      "18A25"
    ],
    "keywords": [
      "configuration space",
      "twisted algebras",
      "persistence",
      "cohomology",
      "unit disks"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 45,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}