ORIENTABILITY OF FREDHOLM FAMILIES AND TOPOLOGICAL-DEGREE FOR ORIENTABLE NONLINEAR FREDHOLM MAPPINGS

We construct a degree theory for oriented Fredholm mappings of index z ero between open subsets of Banach spaces and between Banach manifolds . Our approach is based on the orientation of Fredholm mappings it doe s not use Fredholm structures on the domain and target spaces. We prov ide a computable formula for the change in degree through an admissibl e homotopy that is necessary for applications to global bifurcation. T he notion of orientation enables us to establish rather precise relati onships between our degree and many other degree theories for particul ar classes of Fredholm maps, including the Elworthy-Tromba degree, whi ch have appeared in the literature in a seemingly unrelated manner. (C ) 1994 Academic Press, Inc.