Derived coisotropic structures II: stacks and quantization

Abstract

We extend results about $n$-shifted coisotropic structures from part I of this work to the setting of derived Artin stacks. We show that an intersection of coisotropic morphisms carries a Poisson structure of shift one less. We also compare non-degenerate shifted coisotropic structures and shifted Lagrangian structures and show that there is a natural equivalence between the two spaces in agreement with the classical result. Finally, we define quantizations of $n$-shifted coisotropic structures and show that they exist for $n>1$.

45 pages. Contains the second half of arXiv:1608.01482v1 with new material added

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• The rational homotopy of mapping spaces of E${}_n$ operads
• Non-formality of the Swiss-Cheese operad
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Cited by in corpus (13)

• Multiplicative Hitchin Systems and Supersymmetric Gauge Theory
• Shifted Coisotropic Correspondences
• Structures symplectiques et de Poisson sur les champs en catégories
• Calabi-Yau structures for multiplicative preprojective algebras
• Quantisation of derived Poisson structures
• Shifted Poisson structures on differentiable stacks
• Derived gluing construction of chiral algebras
• On Quantum Obstruction Spaces and Higher Codimension Gauge Theories
• A note on étale atlases for Artin stacks and Lie groupoids, Poisson structures and quantisation
• Shifted bisymplectic and double Poisson structures on non-commutative derived prestacks
• Shifted coisotropic structures for differentiable stacks
• Deformation Quantization via Categorical Factorization Homology
• Deformation Quantization for Supermanifolds via Gelfand-Kazhdan Descent