{
  "id": "2307.06227",
  "version": "v1",
  "published": "2023-07-12T15:18:55.000Z",
  "updated": "2023-07-12T15:18:55.000Z",
  "title": "New examples of Z/2 harmonic 1-forms and their deformations",
  "authors": [
    "Andriy Haydys",
    "Rafe Mazzeo",
    "Ryosuke Takahashi"
  ],
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "We collect a number of elementary constructions of $\\mathbb Z_2$ harmonic $1$-forms, and of families of these objects. These examples show that the branching set $\\Sigma$ of a $\\mathbb Z_2$ harmonic 1-form may exhibit the following features: i) $\\Sigma$ may be a non-trivial link; ii) $\\Sigma$ may be a multiple cover; iii) $\\Sigma$ may be immersed, and appear as a limit of smoothly embedded branching loci; iv) there are families of $\\mathbb Z_2$ harmonic $1$-forms whose branching sets $\\Sigma$ have tangent cones filling out a positive dimensional space, even modulo isometries.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-12T15:18:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "deformations",
      "branching set",
      "positive dimensional space",
      "elementary constructions",
      "tangent cones"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}