Coincidence index for fiber-preserving maps an approach to stable cohomotopy

A Coincidence index in any generalized (multiplicative) cohomology theory is defined for certain pairs of maps between euclidean neighborhood retracts over a metric space B. By taking an adequate geometric equivalence relation between two such coincidence situations, groups FIXk (B) and FIXk (B,A), for A closed in B, k an integer, can be defined. The purpose of this paper is to show that these groups constitute a generalized multiplicative cohomology theory. Moreover, we show that the index determines an isomorphism between this theory and stable cohomotopy.