{
  "id": "1110.6608",
  "version": "v1",
  "published": "2011-10-30T13:57:15.000Z",
  "updated": "2011-10-30T13:57:15.000Z",
  "title": "On the cohomology of the free loop space of a complex projective space",
  "authors": [
    "Nora Seeliger"
  ],
  "comment": "revised version",
  "categories": [
    "math.AT"
  ],
  "abstract": "Let $\\Lambda (\\mathbb{C}P^n)$ denote the free loop space of the complex projective space $\\mathbb{C}P^n$, i. e. $\\mathbb{C}P^n$ is the projective space of the vector space $\\mathbb{C}^{n+1}$ of dimension $n+1$ over the complex numbers $\\mathbb{C}$ and $\\Lambda(\\mathbb{C}P^n)$ is the function space $\\mathrm{map}(S^1,\\mathbb{C}P^n)$ of unbased maps from a circle $S^1$ into $\\mathbb{C}P^n$ topologized with the compact open topology. In this note we show that despite the fact that the natural fibration $\\Omega(\\mathbb{C}P^n)\\hookrightarrow \\Lambda(\\mathbb{C}P^n)\\stackrel{eval}{\\longrightarrow}\\mathbb{C}P^n$ has a cross section its Serre spectral sequence does not collapse: Here $eval$ is the evaluation map at a base point * $\\in \\mathbb{C}P^n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-10-30T13:57:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "free loop space",
      "complex projective space",
      "cohomology",
      "compact open topology",
      "serre spectral sequence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1110.6608S"
    }
  }
}