{"paper":{"title":"A non-locally trivial $\\mathrm{W}^*$-bundle with fixed factorial fibres","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Kiefer Mommaerts","submitted_at":"2026-06-10T14:30:09Z","abstract_excerpt":"In this paper we construct the first example of a non-locally trivial $\\mathrm{W}^*$-bundle whose fibres are all isomorphic to some fixed $\\mathrm{II}_1$ factor. This is achieved by introducing a notion of uniformly having spectral gap for $\\mathrm{W}^*$-bundles. For bundles with fixed factorial fibres, the negation of having this uniform spectral gap property provides an obstruction for being locally trivial. This results in seemingly elementary examples of $\\mathrm{W}^*$-bundles whose fibres are all isomorphic to some fixed factor but that are not locally trivial, even over spaces with cover"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.12134","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.12134/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}