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'Nonlinear pullbacks' of functions and L∞-morphisms for homotopy Poisson structures
- 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.
- Subjects :
- Homotopy category
Homotopy
010102 general mathematics
Fibration
General Physics and Astronomy
Cofibration
01 natural sciences
Regular homotopy
Algebra
n-connected
Homotopy sphere
Mathematics::Category Theory
Homotopy hypothesis
0103 physical sciences
010307 mathematical physics
Geometry and Topology
0101 mathematics
Mathematics::Symplectic Geometry
Mathematical Physics
Mathematics
Subjects
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