{
  "abstract": "Let $\\mathcal B=(B_g)_{g\\in G}$ be a saturated Fell bundle over a countable discrete group, equipped with a spectral triple. We give explicit sufficient conditions for lifting this triple to the reduced cross-sectional C\\Star-algebra $C_r^*(\\mathcal B)$. Using finite projective realizations of the homogeneous Morita equivalence $B_e$-bimodules, we transport the base Dirac operator to the individual fibres and assemble the resulting operators into a fibrewise Dirac operator. We introduce a spectral-regularity condition ensuring bounded commutators and give a sufficient criterion in terms of uniform derivative bounds on smooth factor-system data. Combining the fibrewise operator with a length operator associated with a proper translation-bounded matrix-valued length function yields the lifted spectral triple. When $B_e$ is separable, the lifted triple, with a suitable grading, represents the Kasparov product of the vertical class with the class of the unit-fibre triple. We also establish a summability criterion and sufficient conditions for stability under central cocycle twisting. A range of examples illustrates the scope of the construction, including twisted crossed products, free compact Abelian actions, and Fell bundles with nonfree homogeneous fibres.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15395",
  "author_total": 1,
  "authors": [
    {
      "name": "Stefan Wagner"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7shbaptb1zpaz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15395",
  "fulltext_url": null,
  "id": "7shbaptb1zpaz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.15395",
  "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-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.OA"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7221814630",
  "pdf_url": "https://arxiv.org/pdf/2610.15395",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7shbaptb1zpaz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:06Z",
      "native_id": "2610.15395",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15395"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Spectral geometry of saturated Fell bundles",
  "title_text": "Spectral geometry of saturated Fell bundles",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/7shbaptb1zpaz",
  "venue": "arXiv",
  "versions": []
}