A Lefschetz type homomorphism for coincidence of several maps

Given $p$-maps $f_1, \cdots, f_p : X \to M,$ $p \geq 2,$ 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.