{
  "id": "math/0304209",
  "version": "v1",
  "published": "2003-04-15T22:22:35.000Z",
  "updated": "2003-04-15T22:22:35.000Z",
  "title": "Diophantine geometry over groups and the elementary theory of free and hyperbolic groups",
  "authors": [
    "Zlil Sela"
  ],
  "journal": "Proceedings of the ICM, Beijing 2002, vol. 2, 87--92",
  "categories": [
    "math.GR"
  ],
  "abstract": "We study sets of solutions to equations over a free group, projections of such sets, and the structure of elementary sets defined over a free group. The structre theory we obtain enable us to answer some questions of A. Tarski's, and classify those finitely generated groups that are elementary equivalent to a free group. Connections with low dimensional topology, and a generalization to (Gromov) hyperbolic groups will also be discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-04-15T22:22:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hyperbolic groups",
      "diophantine geometry",
      "elementary theory",
      "free group",
      "low dimensional topology"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......4209S"
    }
  }
}