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
Published inarXiv.org
Main Authors Ku, Yong Ha, Lee, Jong Bum
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 28.04.2014
Subjects
Automorphisms
Crystallography
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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.
ISSN:2331-8422