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

Research output: Contribution to journalArticle

  • Authors:
  • Theodore Voronov


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.

Bibliographical metadata

Original languageEnglish
Pages (from-to)94-110
Number of pages17
JournalJournal of Geometry and Physics
Early online date19 Oct 2016
StatePublished - Jan 2017