{
  "id": "1807.10131",
  "version": "v1",
  "published": "2018-07-26T13:43:11.000Z",
  "updated": "2018-07-26T13:43:11.000Z",
  "title": "Bridge trisections in $\\mathbb{CP}^2$ and the Thom conjecture",
  "authors": [
    "Peter Lambert-Cole"
  ],
  "comment": "30 pages, 16 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "In this paper, we develop new techniques for understanding surfaces in $\\mathbb{CP}^2$ via bridge trisections. Trisections are a novel approach to smooth 4-manifold topology, introduced by Gay and Kirby, that provide an avenue to apply 3-dimensional tools to 4-dimensional problems. Meier and Zupan subsequently developed the theory of bridge trisections for smoothly embedded surfaces in 4-manifolds. The main application of these techniques is a new proof of the Thom conjecture, which posits that algebraic curves in $\\mathbb{CP}^2$ have minimal genus among all smoothly embedded, oriented surfaces in their homology class. This new proof is notable as it completely avoids any gauge theory or pseudoholomorphic curve techniques.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-26T13:43:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R17",
      "57R40"
    ],
    "keywords": [
      "bridge trisections",
      "thom conjecture",
      "pseudoholomorphic curve techniques",
      "novel approach",
      "gauge theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}