“Nonlinear pullbacks” of functions and -morphisms for homotopy Poisson structures

详细信息    查看全文

• 作者：Theodore Th. Voronov ; ^{theodore.voronov@manchester.ac.uk} ;
• 关键词：58A99 ; 70H15 ; 58C50 ; 58D15 ; 17B55
• 刊名：Journal of Geometry and Physics
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：111
• 期：Complete
• 页码：94-110
• 全文大小：531 K
• 卷排序：111

文摘

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.