The Lefschetz coincidence class of p maps

Abstract

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 1,...,fp : X → Y, p ≥ 2, define a Lefschetz class L(f 1,...,fp ) ∈ H n(p-1)(X;ℚ) and prove that L(f 1,...,fp ) ≠ 0 implies f 1(x) = f 2(x) = ⋯ = fp (x) for some x ∈ X. In the particular case where Y is a homology sphere there are presented some formulas to calculate L(f 1,...,fp ).