# On differential operators over a map, thick morphisms of supermanifolds, and symplectic micromorphisms

@article{Shemyakova2020OnDO,
title={On differential operators over a map, thick morphisms of supermanifolds, and symplectic micromorphisms},
author={Ekaterina Shemyakova and Theodore Th. Voronov},
journal={arXiv: Differential Geometry},
year={2020}
}
• Published 25 September 2020
• Mathematics
• arXiv: Differential Geometry
1 Citations
On a Batalin–Vilkovisky operator generating higher Koszul brackets on differential forms
We introduce a formal $$\hbar$$ -differential operator $$\Delta$$ that generates higher Koszul brackets on the algebra of (pseudo)differential forms on a $$P_{\infty }$$ -manifold. Such an

## References

SHOWING 1-10 OF 20 REFERENCES
Thick morphisms of supermanifolds and oscillatory integral operators
We show that thick morphisms (or microformal morphisms) between smooth (super)manifolds, introduced by us before, are classical limits of 'quantum thick morphisms' defined here as particular
Symplectic microgeometry, IV: Quantization
• Mathematics
Pacific Journal of Mathematics
• 2021
We construct a special class of semiclassical Fourier integral operators whose wave fronts are symplectic micromorphisms. These operators have very good properties: they form a category on which the
Quantization of Forms on the Cotangent Bundle
Abstract:We consider the following construction of quantization. For a Riemannian manifold $M$ the space of forms on T⋆M is made into a space of (full) symbols of operators acting on forms on M. This
Quantum microformal morphisms of supermanifolds: an explicit formula and further properties
We give an explicit formula, as a formal differential operator, for quantum microformal morphisms of (super)manifolds that we introduced earlier. Such quantum microformal morphisms are essentially
Non-linear homomorphisms of algebras of functions are induced by thick morphisms.
In 2014, Voronov introduced the notion of thick morphisms of (super)manifolds as a tool for constructing $L_{\infty}$-morphisms of homotopy Poisson algebras. Thick morphisms generalise ordinary
Microformal Geometry and Homotopy Algebras
• T. Voronov
• Mathematics
Proceedings of the Steklov Institute of Mathematics
• 2018
We extend the category of (super)manifolds and their smooth mappings by introducing a notion of microformal, or “thick,” morphisms. They are formal canonical relations of a special form, constructed
Vector fields on mapping spaces and a converse to the AKSZ construction
The well-known AKSZ construction (for Alexandrov--Kontsevich--Schwarz--Zaboronsky) gives an odd symplectic structure on a space of maps together with a functional $S$ that is automatically a solution
Fourier integral operators. I
Pseudo-differential operators have been developed as a tool for the study of elliptic differential equations. Suitably extended versions are also applicable to hypoelliptic equations, but their value
Graded Geometry, Q‐Manifolds, and Microformal Geometry
We give an exposition of graded and microformal geometry, and the language of Q‐manifolds. Q‐manifolds are supermanifolds endowed with an odd vector field of square zero. They can be seen as a