Algebraic properties of infinite-dimensional differential forms of finite codegree. (Q1432148)

This paper is concerned with the algebraic aspects of the theory of integration over submanifolds of (infinite-dimensional) locally convex spaces or manifolds of finite codimension determined by such submanifolds. The authors derive some identities for differential forms of finite codegree and (classical) differential forms of finite degree. In both cases, the theory of integration should contain objects that can be integrated (namely differential forms), domains of integrations and some measures and/or functions related to these domains. There is a natural duality between construction related to differential forms of finite degree and those related to differential forms of finite codegree.