Epsilon Nielsen fixed point theory

Let [inline-graphic not available: see fulltext] be a map of a compact, connected Riemannian manifold, with or without boundary. For [inline-graphic not available: see fulltext] sufficiently small, we introduce an [inline-graphic not available: see fulltext]-Nielsen number [inline-graphic not available: see fulltext] that is a lower bound for the number of fixed points of all self-maps of [inline-graphic not available: see fulltext] that are [inline-graphic not available: see fulltext]-homotopic to [inline-graphic not available: see fulltext]. We prove that there is always a map [inline-graphic not available: see fulltext] that is [inline-graphic not available: see fulltext]-homotopic to [inline-graphic not available: see fulltext] such that [inline-graphic not available: see fulltext] has exactly [inline-graphic not available: see fulltext] fixed points. We describe procedures for calculating [inline-graphic not available: see fulltext] for maps of [inline-graphic not available: see fulltext]-manifolds.