{
  "id": "0902.2493",
  "version": "v2",
  "published": "2009-02-14T20:35:48.000Z",
  "updated": "2009-02-23T09:28:58.000Z",
  "title": "Makanin-Razborov Diagrams over Free Products",
  "authors": [
    "E. Jaligot",
    "Z. Sela"
  ],
  "categories": [
    "math.GR",
    "math.LO"
  ],
  "abstract": "This paper is the first in a sequence on the first order theory of free products. In the first paper we generalize the analysis of systems of equations over free and (torsion-free) hyperbolic groups, and analyze system of equations over free products. To do that we introduce limit groups over the class of free products, and show that a finitely presented group has a canonical (finite) collection of maximal limit quotients. We further extend this finite collection and associate a Makanin-Razborov diagram over free products with a finitely presented group. This MR diagram encodes all the quotients of a given finitely presented group that are free products, all its homomorphisms into free products, and equivalently all the solutions to a given system of equations over a free product.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-02-23T09:28:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "free product",
      "makanin-razborov diagram",
      "first order theory",
      "maximal limit quotients",
      "mr diagram encodes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0902.2493J"
    }
  }
}