The R_∞ property for crystallographic group of Sol

2014/04/28 by Ku Yong Ha, Ha, Ku Yong, Jong Bum Lee +1
Mathematics · #55M20 #57S30 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals #Mathematics and Applications #math.AT #math.GR #msc:55M20 #msc:57S30

paper · pdf · doi:10.48550/arxiv.1404.6877

25 pages

arxiv created 2014/04/28 · openalex publication_date 2014/04/28 · arxiv updated 2014/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

Related

• The Reidemeister spectrum of low dimensional almost-crystallographic groups
• The R_∞ property for abelian groups
• The R_∞--property for nilpotent quotients of Baumslag--Solitar groups
• Reidemeister numbers for arithmetic Borel subgroups in type A
• On the Reidemeister spectrum and the R_∞ property for some free nilpotent groups