Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2020; 57(4): 909-919

Online first article October 24, 2019      Printed July 31, 2020

https://doi.org/10.4134/BKMS.b190601

Copyright © The Korean Mathematical Society.

Nielsen spectrum of maps on infra-solvmanifolds modeled on $\Sol_0^{\kern2pt 4}$

Jong Bum Lee

Sogang University

Abstract

The 4-dimensional solvable Lie group $\Sol_0^{\kern2pt 4}$ does not admit a lattice. The purpose of this paper is two-fold. We study poly-crystallo\-graphic groups of $\Sol_0^{\kern2pt 4}$, and then we study Nielsen fixed point theory on the spaces modeled on $\Sol_0^{\kern2pt 4}$.

Keywords: Infra-solvmanifold, Lefschetz number, mapping torus, Nielsen number, poly-crystallographic group, Reidemeister number, $\Solof$

MSC numbers: Primary 57S30, 57S20, 22E25

Supported by: The author was partially supported by Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education (NRF2016-R1D1A1B01006971)