Lefschetz coincidence theory for maps between spaces of different dimensions

For a given pair of maps f,g :X→M from an arbitrary topological space to an n-manifold, the Lefschetz homomorphism is a certain graded homomorphism Λfg :H(X)→H(M) of degree (−n). We prove a Lefschetz-type coincidence theorem: if the Lefschetz homomorphism is nontrivial then there is an x∈X such that f(x)=g(x).