Poisson AKSZ theories and their quantizations

@article{JohnsonFreyd2013PoissonAT,
  title={Poisson AKSZ theories and their quantizations},
  author={Theo Johnson-Freyd},
  journal={arXiv: Mathematical Physics},
  year={2013}
}
We generalize the AKSZ construction of topological field theo- ries to allow the target manifolds to have possibly-degenerate up-to-homotopy Poisson structures. Classical AKSZ theories, which exist for all oriented space- times, are described in terms of dioperads. The quantization problem is posed in terms of extending from dioperads to properads. We conclude by relating the quantization problem for AKSZ theories on R d to the formality of the Ed operad, and conjecture a properadic description… 
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