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(2009 / vol.11 / no.1)
Averaging formula for Nielsen numbers
Jong Bum Lee, Kyung Bai Lee
Pages. 71-82   



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 $f:M o
M$ be a continuous map. The averaging formula for Nielsen numbers
$$
N(f) = frac{1}{vertPsivert} sum_{Ain Psi}
vertdet(A_*-f_*)vert
$$
is proved. This is a workable formula for the difficult number
$N(f)$.



1. Introduction
2. Infra-solvmanifolds
3. Linearization of maps on solvmanifolds
4. Averaging formula for Nielsen numbers



Infra-solvmanifolds, Lefschetz numbers, Nielsen numbers



55M20, 57S30