Letters in Mathematical Physics
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.
Jacobi manifold, contact manifold, differential graded manifold, symplectic manifold, Poisson manifold
Mehta, Rajan Amit, "Differential Graded Contact Geometry and Jacobi Structures" (2013). Mathematics and Statistics: Faculty Publications. 17.