Differential graded contact geometry and Jacobi structures

TL;DR

This paper explores the relationship between graded contact structures with homological vector fields and Jacobi manifolds, revealing a supergeometric perspective on the Poissonization process.

Contribution

It establishes a one-to-one correspondence between degree 1 contact structures and Jacobi manifolds, providing a supergeometric reinterpretation of symplectization.

Findings

Degree 1 contact structures correspond to Jacobi manifolds

Poissonization is viewed as supergeometric symplectization

Provides new insights into graded contact geometry

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.