Relatively Hyperbolic Coxeter Groups with maximal Flats of codimension 1

TL;DR

This paper investigates a specific class of relatively hyperbolic Coxeter groups with maximal Euclidean subgroups of codimension 1, establishing an upper bound on their dimension.

Contribution

It provides the first known bound on the dimension of relatively hyperbolic Coxeter groups with maximal flats of codimension 1.

Findings

Dimension of these Coxeter groups is bounded above.

Characterization of maximal Euclidean Coxeter subgroups of codimension 1.

Advances understanding of geometric properties of these groups.

Abstract

We study relatively hyperbolic Coxeter groups of type $HM$ with maximal Euclidean Coxeter subgroups of codimension 1. Our main result in this paper is that the dimension of these groups is bounded above.