Averaging formula for Nielsen numbers of maps on infra-solvmanifolds of type (R)

Abstract

We prove that the averaging formula for Nielsen numbers holds for continuous maps on infra-solvmanifolds of type (R): Let $M$ be such a manifold with holonomy group $\Psi$ and let $f:M \to M$ be a continuous map. The averaging formula for Nielsen numbers

N(f) = \frac{1}{\lvert\Psi\rvert} \sum_{A \in \Psi} \lvert\det(A_{*}-f_{*})\rvert

is proved. This is a workable formula for the difficult number $N(f)$.