An algebraic method for computing N~ε(f)

摘要

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 e-core concept to develop an algebraic method for computing the ε-Nielsen number in some cases.