Cannon-Thurston maps for Coxeter groups including affine special subgroups

TL;DR

This paper investigates Cannon-Thurston maps for Coxeter groups with a focus on those containing affine special subgroups, exploring boundary maps and limit sets in the context of groups with a specific bilinear form signature.

Contribution

It extends the theory of Cannon-Thurston maps to Coxeter groups with affine special subgroups, analyzing boundary behavior and limit sets under specific bilinear form conditions.

Findings

Existence of Cannon-Thurston maps for Coxeter groups with signature (n-1,1)

Characterization of boundary maps for groups with affine special subgroups

Insights into the limit sets of such Coxeter groups

Abstract

For a Coxeter group $W$ we have an associating bi-linear form $B$ on a real vector space. We assume that $B$ has the signature $(n-1,1)$. In this case we have the Cannon-Thurston map for $W$, that is, a $W$-equivariant continuous surjection from the Gromov boundary of $W$ to the limit set of $W$. We focus on the case where Coxeter groups contain affine special subgroups.