3 papers
math.GR2025
Unimodular random graphs with Property (T) have cost one
Łukasz Grabowski, Héctor Jardón-Sánchez, Sam Mellick
Hutchcroft and Pete showed that countably infinite groups with Property (T) admit cost one actions, resolving a question of Gaboriau. We give a streamlined proof of their theorem,…
math.GR2023
On group rings of virtually abelian groups
Joan Claramunt, Lukasz Grabowski
Let be a finitely generated torsion-free group. We show that the statement of being virtually abelian is equivalent to the statement that the -regular closure of the gro…
math.MG2021
On random compact sets, equidecomposition, and domains of expansion in R^3
Tomasz Cieśla, Łukasz Grabowski
We study random compact subsets of R^3 which can be described as "random Menger sponges". We use those random sets to construct a pair of compact sets A and B in R^3 which are of t…