Ideals of the Lie algebras of vector fields
Differential forms on the Fréchet manifold of smooth functions on a compact -dimensional manifold can be obtained in a natural way from pairs of differential forms on and by the hat pairing. Special cases are the transgression map (hat pairing with a constant function) and the bar map (hat pairing with a volume form). We develop a hat calculus similar to the tilda calculus for non-linear Grassmannians [6].
Soit un germe en de 1-forme différentielle holomorphe vérifiant la condition d’intégrabilité . S’il existe un germe d’application holomorphe de dans qui possède les deux propriétés suivantes :a) a une intégrale première formelle,b) la codimension du lieu singulier de est supérieure ou égale à 2,alors a une intégrale première holomorphe.
These notes are intended to provide a self-contained introduction to the basic ideas of finite dimensional Batalin-Vilkovisky (BV) formalism and its applications. A brief exposition of super- and graded geometries is also given. The BV–formalism is introduced through an odd Fourier transform and the algebraic aspects of integration theory are stressed. As a main application we consider the perturbation theory for certain finite dimensional integrals within BV-formalism. As an illustration we present...