Year: 2026
Type: article
Abstract: In this paper, we show that wreath products of groups have linear divergence, and we generalise the argument to permutational wreath products. We also prove that Houghton groups $${\mathcal {H}}_m$$ H m with $$m\ge 2$$ m ≥ 2 and Baumslag-Solitar groups have linear divergence. We explain how to generalise the argument for wreath products so that it holds for halo products of groups whose halo is large-scale commutative. Finally, we show that wreath products of graphs and Diestel-Leader graphs have linear divergence. The argument for Diestel-Leader graphs is further generalised to horocyclic products of proper, geodesically complete, Busemann $$\delta $$ δ -hyperbolic spaces that are uniformly not a quasi-line.
Source: Geometriae Dedicata
Author: Letizia Issini
Institution: University of Geneva
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,090
Funder: Université de Genève
OpenAlex ID: W7128904383