Forms representing forms and linear spaces on hypersurfaces

Residue forms on singular hypersurfaces

Let M be a complex manifold, X ⊂ M a singular hypersurface. We study residues of top-dimensional meromorphic forms with poles along X. Applying resolution of singularities we obtain residue classes either in L -cohomology of X or in the intersection cohomology. The conditions allowing to construct these residue classes coincide. They can be formulated in terms of weight filtration. In the Appen...

Multilinear forms which are products of linear forms

The conditions under which, multilinear forms (the symmetric case and the non symmetric case),can be written as a product of linear forms, are considered. Also we generalize a result due to S.Kurepa for 2n-functionals in a group G.

Nillsen Difference Spaces and Invariant Linear Forms

Representing Charges by Forms

A charge in a compact metric space is a continuous linear functional on the space of normal chains with real coefficients equipped with a modified flat norm topology. Charges form a cochain complex whose cohomology reflects metric, rather than topological, properties of metric spaces. Elaborating on an idea of De Giorgi, we construct a normed graded differential algebra of Lipschitz forms in a ...

Differential Forms on Noncommutative Spaces

This paper is intended as an introduction to noncommutative geometry for readers with some knowledge of abstract algebra and differential geometry. We show how to extend the theory of differential forms to the “noncommutative spaces” studied in noncommutative geometry. We formulate and prove the Hochschild-Kostant-Rosenberg theorem and an extension of this result involving the Connes differential.