Abstract:This article deals with vector valued differential forms on $C^\infty $-manifolds. As a generalization of the exterior product, we introduce an operator that combines $Hom(\bigotimes ^s(W),Z)$-valued forms with $Hom(\bigotimes ^s(V),W)$-valued forms. We discuss the main properties of this operator such as (multi)linearity, associativity and its behavior under pullbacks, push-outs, exterior differentiation of forms, etc. Finally we present applications for Lie groups and fiber bundles.
Keywords: differential forms, exterior product, multilinear algebra
AMS Subject Classification: Primary 58A10; Secondary 15A75, 22E30, 53C05