Incompressibility and global inversion - Balreira, Eduardo Cabral (Topological Methods in Nonlinear Analysis, 2010)
Given a local diffeomorphism fR^n→ R^n, we consider certain incompressibility conditions on the parallelepiped Df(x)([0,1]^n) which imply that the pre-image of an affine subspace is non-empty and has trivial homotopy groups. These conditions are then used to establish criteria for f to be globally invertible, generalizing in all dimensions the previous results of M. Sabatini.