{
  "id": "1505.04184",
  "version": "v1",
  "published": "2015-05-15T19:53:18.000Z",
  "updated": "2015-05-15T19:53:18.000Z",
  "title": "The rational homotopy type of (n-1)-connected (4n-1)-manifolds",
  "authors": [
    "Diarmuid Crowley",
    "Johannes Nordström"
  ],
  "comment": "23 pages",
  "categories": [
    "math.AT",
    "math.GT"
  ],
  "abstract": "We define the Binachi-Massey tensor on the degree n cohomology with rational coefficients of a topological space X as a linear map from a subspace of the fourth tensor power of H^n(X) (determined by the cup product H^n(X) x H^n(X) -> H^{2n}(X)) to H^{4n-1}(X). If M is a closed (n-1)-connected (4n-1)-manifold (and n > 1) then its rational homotopy type is determined by its cohomology algebra and Bianchi-Massey tensor, and M is formal if and only if the Bianchi-Massey tensor vanishes. We use the Bianchi-Massey tensor to show that there are many (n-1)-connected (4n-1)-manifolds that are not formal but have no non-zero Massey products, and to present a classification of simply-connected 7-manifolds up to finite ambiguity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-15T19:53:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55P62",
      "57N65"
    ],
    "keywords": [
      "rational homotopy type",
      "fourth tensor power",
      "non-zero massey products",
      "bianchi-massey tensor vanishes",
      "cohomology algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150504184C"
    }
  }
}