

Cohomological geometry of differential equations
June 15, 2020 15:00, Moscow, online






Nonlinear homomorphisms and thick morphisms
H. M. Khudaverdian^{} 
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Abstract:
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 pullbacks on $C^{\infty}$ functions. These pullbacks are in general nonlinear maps between the algebras of functions which are socalled nonlinear homomorphisms. By definition, this means that their differentials are algebra homomorphisms in the usual sense. The following conjecture was formulated: an arbitrary nonlinear homomorphism of algebras of smooth functions is generated by some thick morphism. We prove here this conjecture in the class of formal functionals. In this way, we extend the wellknown result for smooth maps of manifolds and algebra homomorphisms of $C^{\infty}$ functions and, more generally, provide an analog of classical "functionalalgebraic duality" in the nonlinear setting.
The talk is based on the preprint arXiv:2006.03417
Materials:
20kras.pdf (201.4 Kb)
Language: English

