• Corpus ID: 219401493

# Non-linear homomorphisms of algebras of functions are induced by thick morphisms.

@article{Khudaverdian2020NonlinearHO,
title={Non-linear homomorphisms of algebras of functions are induced by thick morphisms.},
author={Hovhannes M. Khudaverdian},
journal={arXiv: Algebraic Geometry},
year={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 smooth maps, but are not maps themselves. Nevertheless, they induce pull-backs on $C^{\infty}$ functions. These pull-backs are in general non-linear maps between the algebras of functions which are so-called 'non-linear homomorphisms'. By definition, this means that their differentials are algebra…
1 Citations

## References

SHOWING 1-7 OF 7 REFERENCES
The "nonlinear pullback" of functions and a formal category extending the category of supermanifolds
We introduce mappings between function spaces on smooth (super)manifolds, which are generally nonlinear and which generalize the pullbacks with respect to smooth maps. The construction uses canonical
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
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
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
Voronov Microformal geometry and homotopy algebras
• Proc. Steklov Inst. Math
• 2018