Epsilon Nielsen Fixed Point Theory
نویسنده
چکیده
Let f : X → X be a map of a compact, connected Riemannian manifold, with or without boundary. For > 0 sufficiently small, we introduce an -Nielsen number N ( f ) that is a lower bound for the number of fixed points of all self-maps of X that are -homotopic to f . We prove that there is always a map g : X → X that is -homotopic to f such that g has exactlyN ( f ) fixed points. We describe procedures for calculatingN ( f ) for maps of 1-manifolds.
منابع مشابه
A Nielsen theory for intersection numbers
Nielsen theory, originally developed as a homotopy-theoretic approach to fixed point theory, has been translated and extended to various other problems, such as the study of periodic points, coincidence points and roots. In this paper, the techniques of Nielsen theory are applied to the study of intersections of maps. A Nielsen-type number, the Nielsen intersection number NI(f, g), is introduce...
متن کاملObstructions to Homotopy Invariance in Parametrized Fixed Point Theory
In “zero-parameter” or classical Nielsen fixed point theory one studies Fix(f) := {x ∈ X | f(x) = x} where f : X → X is a map. In case X is an oriented compact manifold and f is transverse to the identity map, idX , Fix(f) is a finite set each of whose elements carries a natural sign, ±1, the index of that fixed point. The set Fix(f) is partitioned into Nielsen classes. Adding the indices withi...
متن کاملRemnant properties in Nielsen coincidence theory
We give an extension to coincidence theory of some key ideas from Nielsen fixed point theory involving remnant properties of free group homomorphisms. In particular we extend Wagner’s theorem for computing Reidemeister classes for Wagner characteristic homomorphisms, which allows us to compute doubly twisted conjugacy classes in many cases. We also extend Kim’s method for homomorphisms with bou...
متن کاملFixed Point Theory and the K{theoretic Trace
The relationship between xed point theory and K {theory is explained, both classical Nielsen theory (versus K 0) and 1{parameter xed point theory (versus K 1). In particular, various zeta functions associated with suspension ows are shown to come in a natural way as \traces" of \torsions" of Whitehead and Reidemeister type.
متن کاملEquivariant Nielsen Invariants for Discrete Groups
For discrete groups G, we introduce equivariant Nielsen invariants. They are equivariant analogs of the Nielsen number and give lower bounds for the number of fixed point orbits in the G-homotopy class of an equivariant endomorphism f : X → X. Under mild hypotheses, these lower bounds are sharp. We use the equivariant Nielsen invariants to show that a G-equivariant endomorphism f is G-homotopic...
متن کامل