"Nonlinear pullbacks" of functions and L∞-morphisms for homotopy Poisson structures /T. T. Voronov

Voronov, Theodore Th.
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Источник
Journal of geometry and physics 2017 Vol. 111. P. 94-110
Аннотация
We introduce mappings between spaces of functions on (super)manifolds that generalize pullbacks with respect to smooth maps but are, in general, nonlinear (actually, formal). The construction is based on canonical relations and generating functions. (The underlying structure is a formal category, which is a “thickening” of the usual category of supermanifolds; it is close to the category of symplectic micromanifolds and their micromorphisms considered recently by A. Weinstein and A. Cattaneo–B. Dherin–A. Weinstein.) There are two parallel settings, for even and odd functions. As an application, we show how such nonlinear pullbacks give L∞L∞-morphisms for algebras of functions on homotopy Schouten or homotopy Poisson manifolds.
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статьи в журналах
Резюме
We introduce mappings between spaces of functions on (super)manifolds that generalize pullbacks with respect to smooth maps but are, in general, nonlinear (actually, formal). The construction is based on canonical relations and generating functions. (The underlying structure is a formal category, which is a “thickening” of the usual category of supermanifolds; it is close to the category of symplectic micromanifolds and their micromorphisms considered recently by A. Weinstein and A. Cattaneo–B. Dherin–A. Weinstein.) There are two parallel settings, for even and odd functions. As an application, we show how such nonlinear pullbacks give L∞L∞-morphisms for algebras of functions on homotopy Schouten or homotopy Poisson manifolds.