{
  "id": "1404.4561",
  "version": "v2",
  "published": "2014-04-17T15:41:59.000Z",
  "updated": "2015-02-23T17:46:19.000Z",
  "title": "A Morse-Bott approach to monopole Floer homology and the Triangulation conjecture",
  "authors": [
    "Francesco Lin"
  ],
  "comment": "160 pages, comments are welcome",
  "categories": [
    "math.GT",
    "math.DG"
  ],
  "abstract": "In the present work we generalize the construction of monopole Floer homology due to Kronheimer and Mrowka to the case of a gradient flow with Morse-Bott singularities. Focusing then on the special case of a three-manifold equipped with a spin$^c$ structure isomorphic to its conjugate, we define the counterpart in this context of Manolescu's recent $\\mathrm{Pin}(2)$-equivariant Seiberg-Witten-Floer homology. In particular, we provide an alternative approach to his disproof of the celebrated Triangulation conjecture.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-04-17T15:41:59.000Z",
      "title": "Morse-Bott singularities in monopole Floer homology and the Triangulation conjecture",
      "abstract": "In the present work we generalize the construction of monopole Floer homology due to Kronheimer and Mrowka to the case of a gradient flow with Morse-Bott singularities. Focusing then on the special case of a spin three-manifold, we define the counterpart in this context of Manolescu's recent $\\mathrm{Pin}(2)$-equivariant Seiberg-Witten-Floer homology. In particular, we provide an alternative approach to his disproof of the celebrated Triangulation conjecture.",
      "comment": "142 pages, preliminary version",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-02-23T17:46:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "monopole floer homology",
      "morse-bott singularities",
      "equivariant seiberg-witten-floer homology",
      "celebrated triangulation conjecture",
      "spin three-manifold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 160,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1291416,
      "adsabs": "2014arXiv1404.4561L"
    }
  }
}