Uncountably many quasi-isometric torsion-free groups
Group Theory
2025-11-19 v1
Abstract
We construct uncountably many finitely generated, pairwise non-isomorphic torsion-free groups, all of which fall into the same quasi-isometry class. This is done by considering Schur covering groups and group cohomology, with the necessary geometric ingredient coming from the theory of bounded-valued cohomology.
Keywords
Cite
@article{arxiv.2511.14277,
title = {Uncountably many quasi-isometric torsion-free groups},
author = {Vladimir Vankov},
journal= {arXiv preprint arXiv:2511.14277},
year = {2025}
}
Comments
10 pages. Comments encouraged!