“Nonlinear pullbacks” of functions and L∞-morphisms for homotopy Poisson structures
@article{Voronov2017NonlinearPO, title={“Nonlinear pullbacks” of functions and L∞-morphisms for homotopy Poisson structures}, author={Theodore Th. Voronov}, journal={Journal of Geometry and Physics}, year={2017}, volume={111}, pages={94-110} }
13 Citations
Microformal Geometry and Homotopy Algebras
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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…
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- Mathematics
- 2017
We show how the tangent functor extends naturally from ordinary smooth maps to "microformal" (or "thick") morphisms of supermanifolds, a notion that we introduced earlier. Microformal morphisms…
L-infinity bialgebroids and homotopy Poisson structures on supermanifolds
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We generalize to the homotopy case a result of K. Mackenzie and P. Xu on relation between Lie bialgebroids and Poisson geometry. For a homotopy Poisson structure on a supermanifold $M$, we show that…
Graded Geometry, Q‐Manifolds, and Microformal Geometry
- MathematicsFortschritte der Physik
- 2019
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…
Non-linear homomorphisms of algebras of functions are induced by thick morphisms.
- Mathematics
- 2020
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…
Thick morphisms, higher Koszul brackets, and $L_{\infty}$-algebroids
- Mathematics
- 2018
It is a classical fact in Poisson geometry that the cotangent bundle of a Poisson manifold has the structure of a Lie algebroid. Manifestations of this structure are the Lichnerowicz differential on…
On differential operators over a map, thick morphisms of supermanifolds, and symplectic micromorphisms
- Mathematics
- 2020
Thick morphisms of supermanifolds, quantum mechanics, and spinor representation
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Symplectic microgeometry, IV: Quantization
- MathematicsPacific 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…
Shifted Derived Poisson Manifolds Associated with Lie Pairs
- MathematicsCommunications in Mathematical Physics
- 2019
We study the shifted analogue of the “Lie–Poisson” construction for $$L_\infty $$ L ∞ algebroids and we prove that any $$L_\infty $$ L ∞ algebroid naturally gives rise to shifted derived Poisson…
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