Jacobi bundles and the BFV-complex

2016/01/31 by Hông Vân Lê, Alfonso Giuseppe Tortorella, Alfonso G. Tortorella +1 · 9 citations
Mathematics · Medicine · Physics and Astronomy · #Algebra over a field #Equivalence (formal languages) #Geometric and Algebraic Topology #Hamiltonian (control theory) #Homotopy and Cohomology in Algebraic Topology #Jacobi identity #Lie algebra #Mathematical analysis #Mathematical optimization #Mathematical physics #Mathematics #Ophthalmology and Eye Disorders #Poisson distribution #Pure mathematics #Submanifold #math-ph #math.DG #math.MP #math.SG #msc:16E45 #msc:53D17 #msc:53D35

paper · pdf · doi:10.1016/j.geomphys.2017.07.025

published in Journal of Geometry and Physics 121, 347-377 (Elsevier BV) · v2: 51 pages, added a new section on an obstructed example in the contact setting, final version to appear in J. Geom. Phys., comments still welcome!

openalex created_date 2016/06/24 · openalex publication_date 2017/08/09 · arxiv created 2017/08/19 · arxiv updated 2017/09/04 · openalex updated_date 2026/08/05

Abstract

We extend the construction of the BFV-complex of a coisotropic submanifold from the Poisson setting to the Jacobi setting. In particular, our construction applies in the contact and l.c.s. settings. The BFV-complex of a coisotropic submanifold S controls the coisotropic deformation problem of S under both Hamiltonian and Jacobi equivalence.

Citations

• Variations on Homological Reduction
• Lectures on Integrability of Lie Brackets
• General Theory of Lie Groupoids and Lie Algebroids
• Quantization of Gauge Systems
• Supergroupoids, double structures, and equivariant cohomology
• Symplectic reduction, BRS cohomology, and infinite-dimensional Clifford algebras
• Generalized Lie bialgebroids and Jacobi structures
• Relative formality theorem and quantisation of coisotropic submanifolds
• Renormalization of gauge theories
• Deformations of coisotropic submanifolds and strong homotopy Lie algebroids