{
  "id": "1609.04874",
  "version": "v1",
  "published": "2016-09-15T22:21:19.000Z",
  "updated": "2016-09-15T22:21:19.000Z",
  "title": "Finiteness of Homological Filling Functions",
  "authors": [
    "Joshua W. Fleming",
    "Eduardo Martínez-Pedroza"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "Let $G$ be a group. For any $\\mathbb{Z} G$--module $M$ and any integer $d>0$, we define a function $FV_{M}^{d+1}\\colon \\mathbb{N} \\to \\mathbb{N} \\cup \\{\\infty\\}$ generalizing the notion of $(d+1)$--dimensional filling function of a group. We prove that this function takes only finite values if $M$ is of type $FP_{d+1}$ and $d>0$, and remark that the asymptotic growth class of this function is an invariant of $M$. In the particular case that $G$ is a group of type $FP_{d+1}$, our main result implies that its $(d+1)$-dimensional homological filling function takes only finite values, addressing a question from [12].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-15T22:21:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65",
      "20J05"
    ],
    "keywords": [
      "finite values",
      "finiteness",
      "asymptotic growth class",
      "main result implies",
      "dimensional filling function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}