Chains and forms in compact metric spaces

Abstract

Charges are linear functionals on normal chains in a compact metric space that are continuous with respect to a modified flat norm topology. They define a cohomology which reflects metric, rather than topological, properties of the underlying space. We show that charges can be represented by metric differentiable forms build from tuples of Lipschitz functions, and that the representation is unique on the cohomology level. For specific forms, the wedge products and the products with normal chains define cup and cap products, respectively.