{
  "id": "1803.06325",
  "version": "v1",
  "published": "2018-03-16T17:26:25.000Z",
  "updated": "2018-03-16T17:26:25.000Z",
  "title": "Lie algebras and $v_n$-periodic spaces",
  "authors": [
    "Gijs Heuts"
  ],
  "categories": [
    "math.AT"
  ],
  "abstract": "We consider a homotopy theory obtained from that of pointed spaces by inverting the maps inducing isomorphisms in $v_n$-periodic homotopy groups. The case n = 0 corresponds to rational homotopy theory. In analogy with Quillen's results in the rational case, we prove that this $v_n$-periodic homotopy theory is equivalent to the homotopy theory of Lie algebras in T(n)-local spectra. We also compare it to the homotopy theory of commutative coalgebras in T(n)-local spectra, where it turns out there is only an equivalence up to a certain convergence issue of the Goodwillie tower of the identity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-03-16T17:26:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lie algebras",
      "periodic spaces",
      "periodic homotopy groups",
      "periodic homotopy theory",
      "rational homotopy theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}