{
  "abstract": "We study linear cocycles over ergodic translations of the two-torus acting on Hermitian vector bundles described by unitary sewing matrices. For a continuous invariant complex line subbundle $L$, we prove that $c_1(L) \\ne 0$ obstructs every nonzero measurable eigensection under a measurable phase-coboundary condition. The abstract obstruction holds in every rank, while for rank-two analytic cocycles with a dominated splitting over a Diophantine translation the phase condition is automatic. In that regime the criterion is exact: $L$ carries a nonzero measurable eigensection if and only if $c_1(L)=0$ and the winding vector of the multiplier phase vanishes. When these conditions hold, the realized eigenvalues form a dense coset on a circle; for each such eigenvalue, the eigenspace carried by $L$ is one-dimensional and has a real-analytic nowhere-vanishing generator. We also construct a Liouville example showing that the Diophantine hypothesis cannot be removed. The proof converts the Chern number into a magnetic charge on the universal cover and applies covariance for irrational magnetic translations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.29577",
  "author_total": 1,
  "authors": [
    {
      "name": "Ahmadreza Azimifard"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7f9y5hx2f6jb8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.29577",
  "fulltext_url": null,
  "id": "7f9y5hx2f6jb8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.29577",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DS"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "arxiv",
      "math.SP"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7214381761",
  "pdf_url": "https://arxiv.org/pdf/2609.29577",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7f9y5hx2f6jb8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.29577",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.29577"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "A Chern-Class Obstruction to Measurable Eigensections of Analytic Quasi-Periodic Bundle Cocycles",
  "title_text": "A Chern-Class Obstruction to Measurable Eigensections of Analytic Quasi-Periodic Bundle Cocycles",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/7f9y5hx2f6jb8",
  "venue": "arXiv",
  "versions": []
}