{
  "id": "1510.05195",
  "version": "v1",
  "published": "2015-10-18T03:12:13.000Z",
  "updated": "2015-10-18T03:12:13.000Z",
  "title": "Homotopy groups of highly connected manifolds",
  "authors": [
    "Samik Basu",
    "Somnath Basu"
  ],
  "categories": [
    "math.AT"
  ],
  "abstract": "In this paper we give a formula for the homotopy groups of $(n-1)$-connected $2n$-manifolds as a direct sum of homotopy groups of spheres in the case the $n^{th}$ Betti number is larger than $1$. We demonstrate that when the $n^{th}$ Betti number is $1$ the homotopy groups might not have such a decomposition. The techniques used in this computation also yield formulae for homotopy groups of connected sums of sphere products and CW complexes of a similar type. In all the families of spaces considered here, we establish a conjecture of J. C. Moore.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-18T03:12:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "homotopy groups",
      "highly connected manifolds",
      "betti number",
      "similar type",
      "direct sum"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151005195B"
    }
  }
}