{
  "id": "0812.2092",
  "version": "v1",
  "published": "2008-12-11T07:51:27.000Z",
  "updated": "2008-12-11T07:51:27.000Z",
  "title": "A limit approach to group homology",
  "authors": [
    "Ioannis Emmanouil",
    "Roman Mikhailov"
  ],
  "journal": "Journal of Algebra, 319, (2008), 1450-1461",
  "categories": [
    "math.GR",
    "math.KT"
  ],
  "abstract": "In this paper, we consider for any free presentation $G = F/R$ of a group $G$ the coinvariance $H_{0}(G,R_{ab}^{\\otimes n})$ of the $n$-th tensor power of the relation module $R_{ab}$ and show that the homology group $H_{2n}(G,{\\mathbb Z})$ may be identified with the limit of the groups $H_{0}(G,R_{ab}^{\\otimes n})$, where the limit is taken over the category of these presentations of $G$. We also consider the free Lie ring generated by the relation module $R_{ab}$, in order to relate the limit of the groups $\\gamma_{n}R/[\\gamma_{n}R,F]$ to the $n$-torsion subgroup of $H_{2n}(G,{\\mathbb Z})$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-12-11T07:51:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "group homology",
      "limit approach",
      "relation module",
      "th tensor power",
      "free presentation"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0812.2092E"
    }
  }
}