{
  "id": "0909.3222",
  "version": "v4",
  "published": "2009-09-17T13:54:03.000Z",
  "updated": "2010-10-08T13:44:42.000Z",
  "title": "Uniqueness of $A_\\infty$-structures and Hochschild cohomology",
  "authors": [
    "Constanze Roitzheim",
    "Sarah Whitehouse"
  ],
  "comment": "The paper has been rearranged and the results are now formulated in terms of a filtration of the Hochschild cohomology groups. To appear in Algebraic and Geometric Topology",
  "categories": [
    "math.AT"
  ],
  "abstract": "This paper investigates if a differential graded algebra can have more than one $A_\\infty$-structure extending the given differential graded algebra structure. We give a sufficient condition for uniqueness of such an $A_\\infty$-structure up to quasi-isomorphism using Hochschild cohomology. We then extend this condition to Sagave's notion of derived $A_\\infty$-algebras after introducing a notion of Hochschild cohomology that applies to this.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2010-10-08T13:44:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "18E30",
      "55U35"
    ],
    "keywords": [
      "hochschild cohomology",
      "uniqueness",
      "differential graded algebra structure",
      "sagaves notion",
      "sufficient condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0909.3222R"
    }
  }
}