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PreprintCC BY-NC-ND 4.0arXiv

The shifted symplectic geometry of derived higher groupoids

  • Miquel Cueca
  • Florian Dorsch
  • Reyer Sjamaar
  • Chenchang Zhu
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Abstract

The main goal of this work is to introduce derived Lie n-groupoids and their shifted symplectic structures. We further define shifted lagrangian structures and prove that their composition is well defined under suitable conditions. As an application, we show that our framework incorporates several reduction procedures at critical values, including: classical Hamiltonian reduction, group valued moment maps, Poisson Lie group valued moment maps and Mikami-Weinstein for proper symplectic groupoids.

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Cite

BibTeXRIS
BibTeX
@misc{cueca2026shifted,
  title = {{The shifted symplectic geometry of derived higher groupoids}},
  author = {Miquel Cueca and Florian Dorsch and Reyer Sjamaar and Chenchang Zhu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2607.17362},
  eprint = {2607.17362},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.17362},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - The shifted symplectic geometry of derived higher groupoids
AU  - Miquel Cueca
AU  - Florian Dorsch
AU  - Reyer Sjamaar
AU  - Chenchang Zhu
PY  - 2026
DA  - 2026/10/22
PB  - arXiv
DO  - 10.48550/arxiv.2607.17362
UR  - https://arxiv.org/abs/2607.17362
AB  - The main goal of this work is to introduce derived Lie n-groupoids and their shifted symplectic structures. We further define shifted lagrangian structures and prove that their composition is well defined under suitable conditions. As an application, we show that our framework incorporates several reduction procedures at critical values, including: classical Hamiltonian reduction, group valued moment maps, Poisson Lie group valued moment maps and Mikami-Weinstein for proper symplectic groupoids.
ER  -