{
  "id": "1912.03843",
  "version": "v1",
  "published": "2019-12-09T04:32:49.000Z",
  "updated": "2019-12-09T04:32:49.000Z",
  "title": "Homological perturbation theory with curvature",
  "authors": [
    "Matthew Hogancamp"
  ],
  "comment": "20 pages",
  "categories": [
    "math.AT"
  ],
  "abstract": "We prove a general version of the homological perturbation lemma which works in the presence of curvature, and without the restriction to strong deformation retracts, building on work of Markl. A key observation is that the notion of strong homotopy equivalence of complexes (or objects in an abstract dg category) has a natural expression in the language of curved twisted complexes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-09T04:32:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "homological perturbation theory",
      "strong deformation retracts",
      "strong homotopy equivalence",
      "abstract dg category",
      "homological perturbation lemma"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}