Back to Search Start Over

'Nonlinear pullbacks' of functions and L∞-morphisms for homotopy Poisson structures

Authors :
Theodore Voronov
Source :
Journal of Geometry and Physics. 111:94-110
Publication Year :
2017
Publisher :
Elsevier BV, 2017.

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 L ∞ -morphisms for algebras of functions on homotopy Schouten or homotopy Poisson manifolds.

Details

ISSN :
03930440
Volume :
111
Database :
OpenAIRE
Journal :
Journal of Geometry and Physics
Accession number :
edsair.doi...........1548f0775dcf74256a8b905d155c7c89
Full Text :
https://doi.org/10.1016/j.geomphys.2016.10.004