An algebraic method for computing Nϵ(f)Nϵ(f)

Let f:X→Xf: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 Nϵ(f)Nϵ(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.