{
  "id": "1810.09716",
  "version": "v1",
  "published": "2018-10-23T08:22:34.000Z",
  "updated": "2018-10-23T08:22:34.000Z",
  "title": "$\\ell^2$-Betti numbers of random rooted simplicial complexes",
  "authors": [
    "Michael Schrödl"
  ],
  "categories": [
    "math.AT"
  ],
  "abstract": "We define unimodular measures on the space of rooted simplicial complexes and associate to each measure a chain complex and a trace function. As a consequence, we can define $\\ell^2$-Betti numbers of unimodular random rooted simplicial complexes and show that they are continuous under Benjamini-Schramm convergence.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-23T08:22:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55U10",
      "05A16"
    ],
    "keywords": [
      "betti numbers",
      "unimodular random rooted simplicial complexes",
      "define unimodular measures",
      "chain complex",
      "trace function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}