"Nonlinear Pullbacks" of Functions and L-infinity Morphisms for Homotopy Poisson Structures

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    Abstract

    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 L1-morphisms for algebras of functions on homotopy Schouten or homotopy Poisson manifolds.
    Original languageEnglish
    Pages (from-to)94-110
    Number of pages17
    JournalJournal of Geometry and Physics
    Volume111
    Early online date19 Oct 2016
    DOIs
    Publication statusPublished - Jan 2017

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