Differential graded contact geometry and Jacobi structures
Symplectic Geometry
2013-08-20 v4 Differential 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.
Cite
@article{arxiv.1111.4705,
title = {Differential graded contact geometry and Jacobi structures},
author = {Rajan Amit Mehta},
journal= {arXiv preprint arXiv:1111.4705},
year = {2013}
}
Comments
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