An algebraic method for computing

Let f : X → X be a smooth self-map on a compact connected Riemannian manifold X, with or without boundary. We introduce a subset of the ϵ-homotopy set of f, which we call the ϵ-core of f, on which the ϵ-Nielsen number N ϵ ( f ) of f is homotopy invariant. We use the ϵ-core concept to develop an algebraic method for computing the ϵ-Nielsen number in some cases.