{
  "id": "2409.03967",
  "version": "v1",
  "published": "2024-09-06T01:36:24.000Z",
  "updated": "2024-09-06T01:36:24.000Z",
  "title": "Covers of surfaces",
  "authors": [
    "Ian Biringer",
    "Yassin Chandran",
    "Tommaso Cremaschi",
    "Jing Tao",
    "Nicholas G. Vlamis",
    "Mujie Wang",
    "Brandis Whitfield"
  ],
  "categories": [
    "math.GT"
  ],
  "abstract": "We study the homeomorphism types of certain covers of (always orientable) surfaces, usually of infinite-type. We show that every surface with non-abelian fundamental group is covered by every noncompact surface, we identify the universal abelian covers and the $\\mathbb{Z}/n\\mathbb{Z}$-homology covers of surfaces, and we show that non-locally finite characteristic covers of surfaces have four possible homeomorphism types.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-09-06T01:36:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "homeomorphism types",
      "non-abelian fundamental group",
      "non-locally finite characteristic covers",
      "universal abelian covers",
      "homology covers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}