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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… Expand

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… Expand

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… Expand

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… Expand

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… Expand