{
  "id": "2010.04318",
  "version": "v1",
  "published": "2020-10-09T01:30:42.000Z",
  "updated": "2020-10-09T01:30:42.000Z",
  "title": "Monopoles and Landau-Ginzburg Models III: A Gluing Theorem",
  "authors": [
    "Donghao Wang"
  ],
  "comment": "52 pages, 12 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "This is the third paper of this series. In an earlier work, the author defined the monopole Floer homology for any pair $(Y,\\omega)$, where $Y$ is an oriented 3-manifold with toroidal boundary and $\\omega$ is a suitable closed 2-form. In this paper, we establish a gluing theorem for this Floer homology when two such 3-manifolds are glued suitably along their common boundary, assuming that $\\partial Y$ is disconnected and $\\omega$ is non-vanishing on $\\partial Y$. As applications, we construct the monopole Floer 2-functor and the generalized cobordism maps. Using results of Kronheimer-Mrowka and Ni, we prove that for any such 3-manifold $Y$ that is irreducible, this Floer homology detects the Thurston norm on $H_2(Y,\\partial Y;\\mathbb{R})$ and the fiberness of $Y$. Finally, we show that our construction recovers the monopole link Floer homology for any link inside a closed 3-manifold.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-09T01:30:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R58"
    ],
    "keywords": [
      "gluing theorem",
      "landau-ginzburg models",
      "monopole link floer homology",
      "floer homology detects",
      "monopole floer homology"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 52,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}