The Pullback Equation for Differential Forms

An important question in geometry and analysis is to know when two k-forms f and g are equivalent through a change of variables. The problem is therefore to find a map I so that it satisfies the pullback equation: I *(g) = f. In more physical terms, the question under consideration can be seen as a problem of mass transportation. The problem has received considerable attention in the cases k = 2 and k = n, but much less when 3 ae k ae n-1. The present monograph provides the first comprehensive study of the equation. The work begins by recounting various properties of exterior forms and differe