Higher-rank GBS groups: non-positive curvature and biautomaticity

TL;DR

This paper characterizes the conditions under which higher-rank generalized Baumslag-Solitar groups are CAT(0) spaces and biautomatic, providing insights into their geometric and algorithmic properties.

Contribution

It offers a complete characterization of when these groups are CAT(0) and biautomatic, advancing understanding of their geometric group theory.

Findings

Identifies criteria for CAT(0) property in higher-rank GBS groups

Determines conditions for biautomaticity in these groups

Provides a framework linking algebraic structure to geometric properties

Abstract

We characterise when a rank $n$ generalised Baumslag-Solitar group is CAT(0) and when it is biautomatic.