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

By: Voronov, Theodore ThMaterial type: ArticleArticleSubject(s): гомотопическая топология | Пуассона структурыGenre/Form: статьи в журналахOnline resources: Click here to access online In: Journal of geometry and physics Vol. 111. P. 94-110Abstract: 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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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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