{"paper":{"title":"Connections on a principal Lie groupoid bundle and representations up to homotopy","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.DG","authors_text":"Naga Arjun S J, Saikat Chatterjee","submitted_at":"2025-02-04T12:50:56Z","abstract_excerpt":"A Lie groupoid principal $\\mbbX$ bundle is a surjective submersion $\\pi\\colon P\\to M$ with an action of $\\mathbb{X}$ on $P$ with certain additional conditions. This paper offers a suitable definition for the notion of a connection on such bundles. Although every Lie groupoid $\\mathbb{X}$ has its associated Lie algebroid $A:=1^*\\ker ds\\to X_0$, it does not admit a natural action on its Lie algebroid. There is no natural action of $\\mathbb{X}$ on $TP$ either. Choosing a connection $\\mathbb{H}\\subset TX_1$ on the Lie groupoid $\\mathbb{X},$ and considering its induced action up to homotopy of $\\ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.02284","kind":"arxiv","version":4},"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/2502.02284/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"}