The $R_\infty$ property for crystallographic group of Sol

There are 9 kinds of crystallographic groups $\Pi$ of Sol. For any automorphism $\varphi$ on $\Pi$, we study the Reidemeister number $R(\varphi)$. Using the averaging formula for the Reidemeister numbers, we prove that most of the crystallographic groups of Sol have the $R_\infty$ property.

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Bibliographic Details
Main Authors Ha, Ku Yong, Lee, Jong Bum
Format Journal Article
LanguageEnglish
Published 28.04.2014
Subjects
Mathematics - Algebraic Topology
Mathematics - Group Theory
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Summary:There are 9 kinds of crystallographic groups $\Pi$ of Sol. For any automorphism $\varphi$ on $\Pi$, we study the Reidemeister number $R(\varphi)$. Using the averaging formula for the Reidemeister numbers, we prove that most of the crystallographic groups of Sol have the $R_\infty$ property.
DOI:10.48550/arxiv.1404.6877