Coxeter galaxy
The preprint "The galaxy of Coxeter groups" by Yuri Santos Rego and Petra Schwer has been recently uploaded to the arXiv!
Link to the paper: arXiv:2211.17038
Abstract:
In this paper we introduce the galaxy of Coxeter groups -- an infinite dimensional, locally finite, ranked simplicial complex which captures isomorphisms between Coxeter systems. In doing so, we would like to suggest a new framework to study the isomorphism problem for Coxeter groups. We prove some structural results about this space, provide a full characterization in small ranks and propose many questions. In addition we survey known tools, results and conjectures. Along the way we show profinite rigidity of triangle Coxeter groups -- a result which is possibly of independent interest.