{
  "id": "math/0508370",
  "version": "v3",
  "published": "2005-08-19T15:17:38.000Z",
  "updated": "2006-09-19T19:52:38.000Z",
  "title": "L^2-Betti numbers of one-relator groups",
  "authors": [
    "Warren Dicks",
    "Peter A. Linnell"
  ],
  "comment": "18 pages, version 3, minor changes. To appear in Math. Ann",
  "journal": "Math. Ann. 337 (2007), no. 4, 855-874",
  "doi": "10.1007/s00208-006-0058-y",
  "categories": [
    "math.GR",
    "math.GT"
  ],
  "abstract": "We determine the L^2-Betti numbers of all one-relator groups and all surface-plus-one-relation groups (surface-plus-one-relation groups were introduced by Hempel who called them one-relator surface groups). In particular we show that for all such groups G, the L^2-Betti numbers b_n^{(2)}(G) are 0 for all n>1. We also obtain some information about the L^2-cohomology of left-orderable groups, and deduce the non-L^2 result that, in any left-orderable group of homological dimension one, all two-generator subgroups are free.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2006-09-19T19:52:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F05",
      "16S34",
      "20J05"
    ],
    "keywords": [
      "one-relator groups",
      "surface-plus-one-relation groups",
      "one-relator surface groups",
      "left-orderable group",
      "two-generator subgroups"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......8370D"
    }
  }
}