Jacobian Conjecture and semi-algebraic maps

Abstract

AbstractLetF:${\mathbb R}$n→${\mathbb R}$nbe a polynomial local diffeomorphism and letSFdenote the set of not proper points ofF. The Jelonek's real Jacobian Conjecture states that if codim(SF) ≥ 2, thenFis bijective. In this work we prove a weak version of such Conjecture, but for more general maps than polynomial, namely: the semi-algebraic maps.