THE FIXED-POINT INDEX FOR THE CLASS OF COMPOSITIONS OF ACYCLIC SET-VALUED MAPS ON ANR-S

In this paper we provide a definition of the fixed-point index of morp hisms defined on arbitrary absolute neighbourhood retracts. This index satisfies all the axioms and yields the unique fixed-point index theo ry for set-valued maps determined by morphisms that is, in particular, for compositions of acyclic maps. The presented approach, which combi nes the homological method with the homotopical one, is based on the h omotopy classification results established in [26] and gives a much si mpler alternative for the fixed-point index theory introduced by SIEGB ERG and SKORDEV [33].