Abstract:

The claim "a local self-diffeomorphism of $R^n$ is globally injective if the pre-image of every hyperplane is connected" has been known as the Nollet-Xavier conjecture after a paper of 2002 by Nollet and Xavier. The validity of this conjecture implies the validity of the Jacobian conjecture. In this lecture we discuss the problem of global inversion of local self-diffeomophisms of $R^n$ and present a counterexamle to the Nollet-Xavier conjecture.

This is joint work with L.R.G. Dias and J. Venato-Santos.

Slides of the talk