Minimal component numbers of fixed point sets
Volume 179 / 2003
Fundamenta Mathematicae 179 (2003), 61-68
MSC: 55M20, 54H25.
DOI: 10.4064/fm179-1-5
Abstract
Let $f\colon (X,A)\to (X,A)$ be a relative map of a pair of compact polyhedra. We introduce a new relative homotopy invariant $N^{\rm C}(f;X,A)$, which is a lower bound for the component numbers of fixed point sets of the self-maps in the relative homotopy class of $f$. Some properties of $N^{\rm C}(f;X,A)$ are given, which are very similar to those of the relative Nielsen number $N(f;X,A)$.
