{
  "id": "2210.08310",
  "version": "v1",
  "published": "2022-10-15T14:32:49.000Z",
  "updated": "2022-10-15T14:32:49.000Z",
  "title": "Formality and finiteness in rational homotopy theory",
  "authors": [
    "Alexander I. Suciu"
  ],
  "comment": "81 pages; prepared for a volume dedicated to Dennis Sullivan's 80th birthday",
  "categories": [
    "math.AT"
  ],
  "abstract": "We explore various formality and finiteness properties in the differential graded algebra models for the Sullivan algebra of piecewise polynomial rational forms on a space. The 1-formality property of the space may be reinterpreted in terms of the filtered and graded formality properties of the Malcev Lie algebra of its fundamental group, while some of the finiteness properties of the space are mirrored in the finiteness properties of algebraic models associated with it. In turn, the formality and finiteness properties of algebraic models have strong implications on the geometry of the cohomology jump loci of the space. We illustrate the theory with examples drawn from complex algebraic geometry, actions of compact Lie groups, and 3-dimensional manifolds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-15T14:32:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55P62",
      "20F14",
      "20F40",
      "55N25"
    ],
    "keywords": [
      "rational homotopy theory",
      "finiteness properties",
      "algebraic models",
      "piecewise polynomial rational forms",
      "complex algebraic geometry"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 81,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}