Voronov Th. On thick morphisms of (super)manifolds (abstract)

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Speaker: Theodore Voronov

Title: On thick morphisms of (super)manifolds

I will tell about a natural generalization of smooth maps, which came about in relation with homotopy Poisson brackets. The key feature of such "thick" or "microformal" morphisms is that they, like usual maps, induce pull-backs of functions; however, unlike the familiar case, such pull-backs are nonlinear. They are, actually, formal nonlinear differential operators of special sort. Thick morphisms make a formal category (i.e., the composition law is formal), which a formal thickening of the ordinary category of smooth supermanifolds and smooth maps. They provide a nonlinear version of the classical functional-algebraic duality between spaces and algebras, where ordinary algebra homomorphisms are replaced by certain "nonlinear homomorphisms". A quantum version of the theory exists, based on some formal Fourierv integral operators.

Slides: VoronovAMVconf2021slides.pdf

Event: Diffieties, Cohomological Physics, and Other Animals, 13-17 December 2021, Moscow.
Alexandre Vinogradov Memorial Conference.