A Lefschetz type homomorphism for coincidence of several maps

Abstract

Given $p$-maps $f_1,\cdots ,f_p:X\to M,$ $p\ge 2,$ from an arbitrary topological space to an orientable closed connected $m$-manifold, in this paper we define a graded homomorphism ${\Lambda }_{f_1\cdots f_p}:H(X)\to H(M^{p-1})$ of degree $-m(p-1)$ called by Lefschetz homomorphism. If the Lefschetz homomorphism is nontrivial then there is a point $x\in X$ such that $f_1(x)=\cdots =f_p(x).$ The Lefschetz homomorphism ${\Lambda }_{f_1\cdots f_p}$ can be represented as a Knill-like trace.