Seminar talk, 15 June 2020

Speaker: Hovhannes Khudaverdian

Title: Non-linear homomorphisms and thick morphisms

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 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 homomorphisms in the usual sense. The following conjecture was formulated: an arbitrary non-linear 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 well-known result for smooth maps of manifolds and algebra homomorphisms of $C^{\infty }$ functions and, more generally, provide an analog of classical "functional-algebraic duality" in the non-linear setting.

Language: English

Zoom Meeting at https://us02web.zoom.us/j/84025003593

Meeting ID: 840 2500 3593

Video
Slides: 20kras.pdf

References:
arXiv:2006.03417