{
  "id": "2502.07689",
  "version": "v1",
  "published": "2025-02-11T16:44:41.000Z",
  "updated": "2025-02-11T16:44:41.000Z",
  "title": "Geography of irreducible 4-manifolds with order two fundamental group",
  "authors": [
    "Mihail Arabadji",
    "Porter Morgan"
  ],
  "comment": "36 pages",
  "categories": [
    "math.GT"
  ],
  "abstract": "Let $R$ be a closed, oriented topological 4-manifold whose Euler characteristic and signature are denoted by $e$ and $\\sigma$. We show that if $R$ has order two $\\pi_1$, odd intersection form, and $2e + 3\\sigma \\geq 0$, then for all but seven $(e, \\sigma)$ coordinates, $R$ admits an irreducible smooth structure. We accomplish this by performing a variety of operations on irreducible simply-connected 4-manifolds to build 4-manifolds with order two $\\pi_1$. These techniques include torus surgeries, symplectic fiber sums, rational blow-downs, and numerous constructions of Lefschetz fibrations, including a new approach to equivariant fiber summing.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-02-11T16:44:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fundamental group",
      "odd intersection form",
      "symplectic fiber sums",
      "irreducible smooth structure",
      "euler characteristic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}