Jacobi bundles and the BFV-complex

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.

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!

References in corpus (10)

• Gauge Invariance in Field Theory and Statistical Physics in Operator Formalism
• Lectures on Integrability of Lie Brackets
• On the perturbation lemma, and deformations
• Supergroupoids, double structures, and equivariant cohomology
• Deformations of coisotropic submanifolds and strong homotopy Lie algebroids
• Lie-Rinehart algebras, descent, and quantization
• Generalized Contact Bundles
• Variations on Homological Reduction
• Deformation Theory (lecture notes)
• Rigidity of integral coisotropic submanifolds of contact manifolds

Cited by in corpus (7)

• Holomorphic Jacobi Manifolds and Holomorphic Contact Groupoids
• Infinitesimal Automorphisms of VB-groupoids and algebroids
• Reductions: precontact versus presymplectic
• Rigidity of integral coisotropic submanifolds of contact manifolds
• The Local Structure of Generalized Contact Bundles
• Contact Dual Pairs
• The Deformation $L_{\infty }$ algebra of a Dirac--Jacobi structure