On the concept of orientability for Fredholm maps between real Banach manifolds

Abstract

In [A simple notion of orientability for Fredholm maps of index zero between Banach manifolds and degree, Ann. Sci. Math. Québec 22 (1998), 131–148] we introduced a concept of orientation and topological degree for nonlinear Fredholm maps between real Banach manifolds. In this paper we study properties of this notion of orientation and we compare it with related results due to Elworthy-Tromba and Fitzpatrick-Pejsachowicz-Rabier.