{
  "id": "2008.13089",
  "version": "v1",
  "published": "2020-08-30T04:59:21.000Z",
  "updated": "2020-08-30T04:59:21.000Z",
  "title": "On the additivity of strong homology for locally compact separable metric spaces",
  "authors": [
    "Nathaniel Bannister",
    "Jeffrey Bergfalk",
    "Justin Tatch Moore"
  ],
  "comment": "13 pages. Comments welcome",
  "categories": [
    "math.LO",
    "math.AT"
  ],
  "abstract": "We show that it is consistent relative to a weakly compact cardinal that strong homology is additive and compactly supported within the class of locally compact separable metric spaces. This complements work of Marde\\v{s}i\\'{c} and Prasolov showing that the Continuum Hypothesis implies that a countable sum of Hawaiian earrings witnesses the failure of strong homology to possess either of these properties. Our results build directly on work of Lambie-Hanson and the second author which establishes the consistency, relative to a weakly compact cardinal, of $\\mathrm{lim}^s \\mathbf{A} = 0$ for all $s \\geq 1$ for a certain pro-abelian group $\\mathbf{A}$; we show that that work's arguments carry implications for the vanishing and additivity of the $\\mathrm{lim}^s$ functors over a substantially more general class of pro-abelian groups indexed by $\\mathbb{N}^{\\mathbb{N}}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-30T04:59:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E35",
      "55N07",
      "03E75",
      "55N40"
    ],
    "keywords": [
      "locally compact separable metric spaces",
      "strong homology",
      "additivity",
      "weakly compact cardinal",
      "works arguments carry implications"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}