{
  "abstract": "In this paper, we determine the possible signatures of flat unitary bundles over compact connected oriented surfaces of positive genus with nonempty boundary. More precisely, if $\\Sigma_{g,n}$ has genus $g\\geq 1$ and $n\\geq 1$ boundary components, then the signatures arising from representations $\\pi_1(\\Sigma_{g,n})\\to\\mathrm{U}(p,q)$ are exactly the integers $m$ satisfying \\[ |m| \\leq (p+q)(2g+n-2) -(2g-2)|p-q| -\\min\\{2,n|p-q|\\}. \\] Every such integer, including the two extremal values, is realized by a block-diagonal representation whose image is contained, after possibly interchanging $p$ and $q$, in $\\mathrm{U}(1,1)^{\\times\\min\\{p,q\\}}\\times\\mathrm{U}(|p-q|)$.",
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  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.15549",
  "author_total": 3,
  "authors": [
    {
      "name": "Inkang Kim"
    },
    {
      "name": "Pierre Pansu"
    },
    {
      "name": "Xueyuan Wan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fwnfef1mrv3rr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.15549",
  "fulltext_url": null,
  "id": "fwnfef1mrv3rr",
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  "landing_url": "https://hal.science/hal-05748505v1",
  "language": "en",
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
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      "arxiv",
      "math.GT"
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      "0.math"
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  "openalex": "W7213301320",
  "pdf_url": "https://hal.science/hal-05748505/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fwnfef1mrv3rr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:47Z",
      "native_id": "hal-05748505",
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      "url": "https://hal.science/hal-05748505v1"
    },
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.15549",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.15549"
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  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "On possible values of the signature of flat unitary bundles over compact surfaces",
  "title_text": "On possible values of the signature of flat unitary bundles over compact surfaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/fwnfef1mrv3rr",
  "venue": "HAL",
  "versions": []
}