Skip to content
DraconiticResearch
Search Sources API
197,768 studies31 sourcesUpdated 44 min ago
PreprintarXiv licencearXiv

The symplectic leaves of the affine Poisson C∞-scheme associated with a singular subalgebroid

  • Ruben Louis
Open at sourcePDFDOICite

Abstract

Every singular subalgebroid, and in particular every singular foliation 𝒢, determines a universal Poisson C∞-scheme Spec(ℱ(𝒢)), which is the analogue of the linear Poisson structure on the dual of a Lie algebroid. We show that the underlying space Xℱ(𝒢) of Spec(ℱ(𝒢)) decomposes as a disjoint union of symplectic manifolds. Furthermore, we extend the Helffer-Nourrigat cone to a singular subalgebroid and show that it is an embedded Poisson C∞-subscheme of Spec(ℱ(𝒢)).

Related

  1. Symplectic groupoid multiplication and Poisson integrators
    Alejandro Cabrera, David Iglesias Ponte, Juan Carlos Marrero
    arXivPreprintCC BY 4.0Full textGeometry & topologyarXiv
  2. Butcher series for Hamiltonian Poisson integrators through symplectic groupoids
    Adrien Busnot Laurent, Oscar Cosserat
    HALPreprintCC BY 4.0Full textCombinatorics & discrete mathematicsGeometry & topologyHAL
  3. Moduli space of irregular singular λ-connections and the relative symplectic form
    Michi-aki Inaba, Arata Komyo
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  4. Converse symplectic interlacing via low-rank singular value perturbations
    Priyanka Grover, Hemant K. Mishra, Sarishti Singh +1
    arXivPreprintCC BY-NC-ND 4.0Full textAnalysis & PDEsGeometry & topologyarXiv
  5. Symplectic Lie groups and nilmanifolds associated with acyclic quivers
    Yihao Zheng
    arXivPreprintarXiv licenceFull textCombinatorics & discrete mathematicsGeometry & topologyarXiv

Cite

BibTeXRIS
BibTeX
@misc{louis2026symplectic,
  title = {{The symplectic leaves of the affine Poisson $C^\infty$-scheme associated with a singular subalgebroid}},
  author = {Ruben Louis},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.30395},
  eprint = {2610.30395},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.30395},
}
RIS
TY  - UNPB
TI  - The symplectic leaves of the affine Poisson C^∞-scheme associated with a singular subalgebroid
AU  - Ruben Louis
PY  - 2026
DA  - 2026/10/21
PB  - arXiv
DO  - 10.48550/arxiv.2610.30395
UR  - https://arxiv.org/abs/2610.30395
AB  - Every singular subalgebroid, and in particular every singular foliation 𝒢, determines a universal Poisson C^∞-scheme Spec(ℱ(𝒢)), which is the analogue of the linear Poisson structure on the dual of a Lie algebroid. We show that the underlying space X_ℱ(𝒢) of Spec(ℱ(𝒢)) decomposes as a disjoint union of symplectic manifolds. Furthermore, we extend the Helffer-Nourrigat cone to a singular subalgebroid and show that it is an embedded Poisson C^∞-subscheme of Spec(ℱ(𝒢)).
ER  -