The Lefschetz coincidence class of p maps

Abstract

Let X be an arbitrary topological space and let Y be a closed connected oriented n-dimensional manifold. In this work we consider p maps 'F IND.1',..., 'F IND.P' : X → Y , p ≥ 2, define a Lefschetz class L('F IND.1',..., 'F IND.P') 'PERTENCE A' 'H POT.N(P-1)' (X;Q) and prove that L('F IND.1',..., 'F IND.P') ≠ 0 implies 'F IND.1'(x) = 'F IND.2'(x) for some x 'PERTENCE A' X. In the particular case where Y is a homology sphere there are presented some formulas to calculate L('F IND.1',..., 'F IND.P').