On the concept of orientability for Fredholm maps between real Banach manifolds (Q5936107)

In this interesting survey, the authors continue their study of a concept of orientation for nonlinear Fredholm operators between real Banach manifolds previously introduced by the authors in [Ann. Sci. Math. Qué. 22, No. 2, 131-148 (1998; Zbl 1058.58502)], see also the first author, Birkhäuser. Prog. Nonlinear Differ. Equ. Appl. 43, 201-213 (2001; Zbl 1001.47045). The crucial point is the ``stability'' of this notion of orientation with respect to ``small'' changes of the operator. A comparison with the (similar, but different) definition of orientation due to \textit{P. M. Fitzpatrick}, \textit{J. Pejsachowicz} and \textit{P. J. Rabier} [J. Funct. Anal. 124, No. 1, 1-39 (1994; Zbl 0802.47056)] is also given.