Nagoya Mathematical Journal

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

Jong Bum Lee and Kyung Bai Lee

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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 $N(f)$.

Article information

Source
Nagoya Math. J., Volume 196 (2009), 117-134.

Dates
First available in Project Euclid: 15 January 2010

Permanent link to this document
https://projecteuclid.org/euclid.nmj/1263564650

Mathematical Reviews number (MathSciNet)
MR2591093

Zentralblatt MATH identifier
1234.55002

Subjects
Primary: 55M20: Fixed points and coincidences [See also 54H25] 57S30: Discontinuous groups of transformations

Keywords
averaging formula infra-solvmanifolds Nielsen numbers

Citation

Lee, Jong Bum; Lee, Kyung Bai. Averaging formula for Nielsen numbers of maps on infra-solvmanifolds of type (R). Nagoya Math. J. 196 (2009), 117--134. https://projecteuclid.org/euclid.nmj/1263564650


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