{
  "id": "math/9411203",
  "version": "v1",
  "published": "1994-11-07T00:00:00.000Z",
  "updated": "1994-11-07T00:00:00.000Z",
  "title": "Regular Cocycles and Biautomatic Structures",
  "authors": [
    "Walter D. Neumann",
    "Lawrence Reeves"
  ],
  "comment": "Plain Tex, 11 pages, no figures",
  "categories": [
    "math.GR"
  ],
  "abstract": "Let $E$ be a virtually central extension of the group $G$ by a finitely generated abelian group $A$. We show that $E$ carries a biautomatic structure if and only if $G$ has a biautomatic structure $L$ for which the cohomology class of the extension is represented by an $L$-regular cocycle. Moreover, a cohomology class is $L$-regular if some multiple of it is or if its restriction to some finite index subgroup is. We also show that the entire second cohomology of a Fuchsian group is regular, so any virtually central extension is biautomatic. In particular, if the fundamental group of a Seifert fibered 3-manifold is not virtually nilpotent then it is biautomatic. ECHLPT had shown automaticity in this case and in an unpublished 1992 preprint Gersten constructed a biautomatic structure for circle bundles over hyperbolic surfaces and asked if the same could be done for these Seifert fibered 3-manifolds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1994-11-07T00:00:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "biautomatic structure",
      "regular cocycle",
      "virtually central extension",
      "cohomology class",
      "finite index subgroup"
    ],
    "note": {
      "typesetting": "Plain TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1994math.....11203N"
    }
  }
}