Epsilon Nielsen fixed point theory

Abstract

Let be a map of a compact, connected Riemannian manifold, with or without boundary. For sufficiently small, we introduce an -Nielsen number that is a lower bound for the number of fixed points of all self-maps of that are -homotopic to . We prove that there is always a map that is -homotopic to such that has exactly fixed points. We describe procedures for calculating for maps of -manifolds.