PreprintCC BY 4.0arXiv
Moment Lagrangians, unobstructedness and symplectic groupoids
Abstract
Moment Lagrangian Lμ is a Lagrangian in T*G- × Y- × Y associated to a Hamiltonian G-space Y with a moment map μ. In this paper, we prove that Lμ is tautologically unobstructed under mild assumptions on Y. As a key ingredient in the proof, we constructed a new symplectic groupoid structure on T*G- × Y- × Y over G× Y for which Lμ is simultaneously the unit and the fixed locus of the inversion, which might be of independent interest.
Related
- The shifted symplectic geometry of derived higher groupoids
- Butcher series for Hamiltonian Poisson integrators through symplectic groupoids
- Counting Minimal Lagrangians Via Mirzakhani Functions
- Hessian operators, null Lagrangians and the integral comparison principle
- Nearby Lagrangians in the cotangent bundle of the Klein bottle
BibTeX
@misc{li2026moment,
title = {{Moment Lagrangians, unobstructedness and symplectic groupoids}},
author = {Yan-Lung Leon Li},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.12033},
eprint = {2609.12033},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.12033},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Moment Lagrangians, unobstructedness and symplectic groupoids
AU - Yan-Lung Leon Li
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.12033
UR - https://arxiv.org/abs/2609.12033
AB - Moment Lagrangian L_μ is a Lagrangian in T^*G^- × Y^- × Y associated to a Hamiltonian G-space Y with a moment map μ. In this paper, we prove that L_μ is tautologically unobstructed under mild assumptions on Y. As a key ingredient in the proof, we constructed a new symplectic groupoid structure on T^*G^- × Y^- × Y over G× Y for which L_μ is simultaneously the unit and the fixed locus of the inversion, which might be of independent interest.
ER -