Differential graded contact geometry and Jacobi structures

Abstract

We study contact structures on nonnegatively-graded manifolds equipped with homological contact vector fields. In the degree 1 case, we show that there is a one-to-one correspondence between such structures (with fixed contact form) and Jacobi manifolds. This correspondence allows us to reinterpret the Poissonization procedure, taking Jacobi manifolds to Poisson manifolds, as a supergeometric version of symplectization.

9 pages. v2: Added references, improved proof of Proposition 3.3. v3: Expanded introduction, clarifying remarks, some changes of sign conventions. Main results are unchanged. v4: Final version, implementing changes suggested by referees

References in corpus (7)

• Supergroupoids, double structures, and equivariant cohomology
• Introduction to supergeometry
• Graded contact manifolds and contact Courant algebroids
• On homotopy Poisson actions and reduction of symplectic Q-manifolds
• Graded geometry and Poisson reduction
• Contact structures and supersymmetric mechanics
• Jacobi algebroids and quasi Q-manifolds

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• Graded Bundles in the Category of Lie Groupoids
• VB-structures and generalizations
• Contact structures and supersymmetric mechanics
• Higher contact-like structures and supersymmetry
• Multiplicative Connections and Their Lie Theory
• Odd Jacobi manifolds: general theory and applications to generalised Lie algebroids
• Jacobi algebroids and quasi Q-manifolds
• Integrating Nijenhuis Structures
• Generalized symmetries as homotopy Lie algebras
• The Deformation $L_{\infty }$ algebra of a Dirac--Jacobi structure