{
  "abstract": "Let $X$ be a smooth complex projective variety and $D = D_1+\\cdots+D_k\\subset X$ a divisor with simple normal crossings. Consider Deligne's canonical extension $(F,\\nabla)$ of a flat algebraic vector bundle on $X^*:=X\\setminus D$ with unipotent monodromy around every component of $D$. We define and compare the various constructions of the extended Chern-Simons classes $$ \\mathrm{CS}_p(\\nabla^{\\mathrm{Del}})\\;\\in\\; H^{2p-1}(X,\\mathbb{C}/\\mathbb{Z}),\\, p\\geq 1, $$ attached to $(F,\\nabla)$. Our main theorem states that $\\mathrm{CS}_p(\\nabla^{\\mathrm{Del}})$ is torsion in $H^{2p-1}(X,\\mathbb{C}/\\mathbb{Z})$, for every $p\\geq 2$, extending \\cite{Reznikov}, \\cite{Reznikov2}, \\cite{IS-arXiv},\\cite{IS-2div}). We treat the case of quasi-unipotent local monodromies via locally abelian parabolic bundles, and deduce the torsion of Chern-Simons classes. We also extend the Deligne-Sullivan theorem \\cite{DeSu} on triviality of flat bundle on a finite covering of a smooth manifold, to that of a canonical extension, and provide torsion-bounds on the extended characteristic classes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.20877",
  "author_total": 2,
  "authors": [
    {
      "name": "Jaya NN Iyer"
    },
    {
      "name": "Carlos Simpson"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1cy9k64nm1zar.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.20877",
  "fulltext_url": null,
  "id": "1cy9k64nm1zar",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.20877",
  "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.AG"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7204105346",
  "pdf_url": "https://arxiv.org/pdf/2608.20877",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1cy9k64nm1zar.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2608.20877",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.20877"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Torsion of extended Chern-Simons classes for canonical extensions of flat bundles",
  "title_text": "Torsion of extended Chern-Simons classes for canonical extensions of flat bundles",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/1cy9k64nm1zar",
  "venue": "arXiv",
  "versions": []
}