{"paper":{"title":"Automorphisms of Lie groupoids and symplectic reduction on orbifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Symplectic reductions of Hamiltonian étale Lie 2-group actions on orbifolds generally produce symplectic Lie 2-groupoids and remain orbifolds under an isotropic free condition.","cross_cats":["math.SG"],"primary_cat":"math.DG","authors_text":"Bohui Chen, Cheng-Yong Du, Fengyu Jiang","submitted_at":"2026-05-17T09:43:14Z","abstract_excerpt":"In this paper, the 2-group BAut(X) of automorphisms of a Lie groupoid X is constructed. Considering the 2-group G action on X, we explain the equivalence between 2-group homomorphisms from G to BAut(X) with Kan fibrations over G with fiber X. This justifies the notion of Kan fibration for 2-group actions on Lie groupoids. As an application, we formulate Hamiltonian actions of \\'etale Lie 2-groups on orbifolds in terms of Kan fibrations and study the symplectic reductions. We show that, in general, the reduction is in fact a symplectic Lie 2-groupoid, and under certain isotropic free condition,"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We show that, in general, the reduction is in fact a symplectic Lie 2-groupoid, and under certain isotropic free condition, the reduction is still an orbifold. Also the slice theorem of a group G action on Lie groupoids is proved.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The formulation of Hamiltonian actions of étale Lie 2-groups on orbifolds via Kan fibrations over the 2-group, together with the assumption that the symplectic form descends appropriately under the reduction quotient (abstract, section on application to symplectic reductions).","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Constructs automorphism 2-group of Lie groupoids, equates homomorphisms to Kan fibrations, and shows symplectic reductions under étale Lie 2-group Hamiltonian actions yield symplectic Lie 2-groupoids or orbifolds under isotropic free conditions, plus a slice theorem.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Symplectic reductions of Hamiltonian étale Lie 2-group actions on orbifolds generally produce symplectic Lie 2-groupoids and remain orbifolds under an isotropic free condition.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"04ff2ab80058fe9eb159f40c5a625d17915e94a36cbced633ad2c7a0b43d5f01"},"source":{"id":"2605.17351","kind":"arxiv","version":1},"verdict":{"id":"a6f6dc04-b0a5-4d9a-bec6-b81186b7abc0","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T22:58:34.671676Z","strongest_claim":"We show that, in general, the reduction is in fact a symplectic Lie 2-groupoid, and under certain isotropic free condition, the reduction is still an orbifold. Also the slice theorem of a group G action on Lie groupoids is proved.","one_line_summary":"Constructs automorphism 2-group of Lie groupoids, equates homomorphisms to Kan fibrations, and shows symplectic reductions under étale Lie 2-group Hamiltonian actions yield symplectic Lie 2-groupoids or orbifolds under isotropic free conditions, plus a slice theorem.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The formulation of Hamiltonian actions of étale Lie 2-groups on orbifolds via Kan fibrations over the 2-group, together with the assumption that the symplectic form descends appropriately under the reduction quotient (abstract, section on application to symplectic reductions).","pith_extraction_headline":"Symplectic reductions of Hamiltonian étale Lie 2-group actions on orbifolds generally produce symplectic Lie 2-groupoids and remain orbifolds under an isotropic free condition."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.17351/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T23:31:20.089337Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T23:13:08.478991Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T21:41:57.793847Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T21:33:23.726299Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"b4602b6f4ca3fb11e36498e8e4fa45f182fa884c7bd80b36c9bd73c9686f87ce"},"references":{"count":21,"sample":[{"doi":"","year":2007,"title":"A. Adem, J. Leida, and Y. Ruan.Orbifolds and Stringy Topology, volume 171 ofCambridge Tracts in Mathematics. Cambridge University Press, Cambridge, 2007. 22","work_id":"da9b4d35-7d88-4d35-b0e4-757b30a4f56c","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2017,"title":"K. Behrend and E. Getzler. Geometric higher groupoids and categories. In J.-B. Bost, H. Hofer, F. Labourie, Y. L. Jan, X. Ma, and W. Zhang, editors,Geometry, Analysis and Probability, volume 310 ofPro","work_id":"c9534d48-703d-4d6c-83e8-4d3f2c4ce301","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2019,"title":"B. Chen, C.-Y. Du, and R. Wang. The groupoid structure of groupoid morphisms.Journal of Geometry and Physics, 145:103486, 2019. 2, 14","work_id":"0cfe6038-b620-47de-8088-42a90c10bee6","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2013,"title":"M. Crainic and I. Struchiner. On the linearization theorem for proper Lie groupoids.Annales scien- tifiques de l’ ´Ecole normale sup´ erieure, 46(5):723–746, 2013. 36","work_id":"b6fe745c-138c-4456-9402-5afd116a7a4a","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2008,"title":"A. C. da Silva.Lectures on Symplectic Geometry. Number 1764 in Lecture Notes in Mathematics. Springer Berlin Heidelberg, 2008. 43","work_id":"b91de805-ad2f-4374-a753-8913e3457275","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":21,"snapshot_sha256":"65d902e12910ba614f635ebd839eb1c59a1ad85c3d3221e4e34c6f2faadfe1b9","internal_anchors":1},"formal_canon":{"evidence_count":2,"snapshot_sha256":"c37bf6621aa55d656a5a0d923cac3547967b824a1f5a6f4145cab49f6db3bbf2"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}