{
  "id": "2307.08130",
  "version": "v1",
  "published": "2023-07-16T19:04:31.000Z",
  "updated": "2023-07-16T19:04:31.000Z",
  "title": "New constructions and invariants of closed exotic 4-manifolds",
  "authors": [
    "Adam Simon Levine",
    "Tye Lidman",
    "Lisa Piccirillo"
  ],
  "comment": "50 pages, 19 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "In this article, we give new means of constructing and distinguishing closed exotic four-manifolds. Using Heegaard Floer homology, we define new closed four-manifold invariants that are distinct from the Seiberg--Witten and Bauer--Furuta invariants and can remain distinct in covers. Our constructions include exotic definite manifolds with fundamental group $\\mathbb Z/2$, infinite families of exotic manifolds that are related by knot surgeries on Alexander polynomial 1 knots, and exotic manifolds that contain square-zero spheres.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-16T19:04:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57K18",
      "57K41",
      "57R58"
    ],
    "keywords": [
      "closed exotic",
      "constructions",
      "exotic manifolds",
      "contain square-zero spheres",
      "heegaard floer homology"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 50,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}