A relative Nielsen number
Helga Schirmer · Pacific Journal of Mathematics · 1986
A relative Nielsen number N(f; X,A) for a self map /: (X,A) -> (X, A) of a pair of spaces is introduced which shares such properties with the Nielsen number N(f) as homotopy invariance and homotopy type invariance.As N(f; X,A) > N(f) = N(f; X, 0), the relative Nielsen number is in the case A Φ 0 a better lower bound than N(f) for the minimum number MF[f; X,A] of fixed points of all maps in the homotopy class of /.Conditions for a compact polyhedral pair (X, A) are given which ensure that the relative Nielsen number is in fact the best possible lower bound, i.e. that N(f; X, A) = MF[f; X, A].