Pith Number

pith:5YQGCY3B

pith:2026:5YQGCY3B4MAFDGX5VZPLO2VYY3

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Automorphisms of Lie groupoids and symplectic reduction on orbifolds

Bohui Chen, Cheng-Yong Du, Fengyu Jiang

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.

arxiv:2605.17351 v1 · 2026-05-17 · math.DG · math.SG

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4 Citations open

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Claims

C1strongest 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.

C2weakest 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).

C3one 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.

References

21 extracted · 21 resolved · 1 Pith anchors

[1] A. Adem, J. Leida, and Y. Ruan.Orbifolds and Stringy Topology, volume 171 ofCambridge Tracts in Mathematics. Cambridge University Press, Cambridge, 2007. 22 2007

[2] 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 2017

[3] B. Chen, C.-Y. Du, and R. Wang. The groupoid structure of groupoid morphisms.Journal of Geometry and Physics, 145:103486, 2019. 2, 14 2019

[4] 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 2013

[5] A. C. da Silva.Lectures on Symplectic Geometry. Number 1764 in Lecture Notes in Mathematics. Springer Berlin Heidelberg, 2008. 43 2008

Formal links

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Receipt and verification

First computed	2026-05-20T00:03:53.640840Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ee20616361e300519afdae5eb76ab8c6c064919bce356de403df6e3a52588753

Aliases

arxiv: 2605.17351 · arxiv_version: 2605.17351v1 · doi: 10.48550/arxiv.2605.17351 · pith_short_12: 5YQGCY3B4MAF · pith_short_16: 5YQGCY3B4MAFDGX5 · pith_short_8: 5YQGCY3B

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/5YQGCY3B4MAFDGX5VZPLO2VYY3 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: ee20616361e300519afdae5eb76ab8c6c064919bce356de403df6e3a52588753

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c7ccdfb6219f4a0f1912714aaf2768bdfa4d8847676d6ff4b21f6cb6ba658b83",
    "cross_cats_sorted": [
      "math.SG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2026-05-17T09:43:14Z",
    "title_canon_sha256": "3e3542f1a4f5d480e2a140a838c335c6ccb296ebd157194274153b7188a690dd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.17351",
    "kind": "arxiv",
    "version": 1
  }
}