The relative Reidemeister numbers of fiber map pairs

Fernanda S. P. Cardona, Peter N. S. Wong

DOI: http://dx.doi.org/10.12775/TMNA.2003.008

Abstract


The relative Reidemeister number, denoted by $\text{\rm R}(f;X,A)$,
is an upper bound for the relative Nielsen number,
denoted by $\text{\rm N}(f;X,A)$). If $(f,f_{A})$ is a pair of
fibre-preserving maps of a pair of Hurewicz fibrations, then under
certain conditions, the relative Reidemeister number can be
calculated in terms of those on the base and on the fiber. In this
paper, we give addition formulas for $\text{\rm R}(f;X,A)$ and for the relative
Reidemeister number on the complement $\text{\rm R}(f;X-A)$. As an application, we give
estimation of the asymptotic Nielsen type number $text{\rm NI}^{\infty}(f)$.

Keywords


Relative Nielsen number; relative Reidemeister number; fixed points of pairs; fiber-preserving maps; asymptotic Nielsen type number

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