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

Ku Yong Ha; Jong Bum Lee

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

Algebraic Topology 2014-04-29 v1 Group Theory

Authors: Ku Yong Ha , Jong Bum Lee

Abstract

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.

Keywords

crystallographic groups Sol geometry Reidemeister number $R_\infty$ property automorphisms averaging formula

Cite

@article{arxiv.1404.6877,
  title  = {The $R_\infty$ property for crystallographic group of Sol},
  author = {Ku Yong Ha and Jong Bum Lee},
  journal= {arXiv preprint arXiv:1404.6877},
  year   = {2014}
}

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25 pages

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