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Induced differential forms on manifolds of functions

Cornelia Vizman (2011)

Archivum Mathematicum

Differential forms on the Fréchet manifold ℱ ( S , M ) of smooth functions on a compact k -dimensional manifold S can be obtained in a natural way from pairs of differential forms on M and S by the hat pairing. Special cases are the transgression map Ω p ( M ) → Ω p - k ( ℱ ( S , M ) ) (hat pairing with a constant function) and the bar map Ω p ( M ) → Ω p ( ℱ ( S , M ) ) (hat pairing with a volume form). We develop a hat calculus similar to the tilda calculus for non-linear Grassmannians [6].

Intégrales premières d'une forme de Pfaff analytique

Jean-François Mattei, Robert Moussu (1978)

Annales de l'institut Fourier

Soit ω un germe en 0 ∈ C n de 1-forme différentielle holomorphe vérifiant la condition d’intégrabilité ω ∧ d ω = 0 . S’il existe un germe h d’application holomorphe de ( C r , 0 ) dans ( C n , 0 ) qui possède les deux propriétés suivantes :a) h * ( ω ) a une intégrale première formelle,b) la codimension du lieu singulier S ( h * ( ω ) ) de h * ( ω ) est supérieure ou égale à 2,alors ω a une intégrale première holomorphe.

Introduction to Graded Geometry, Batalin-Vilkovisky Formalism and their Applications

Jian Qiu, Maxim Zabzine (2011)

Archivum Mathematicum

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...

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