English

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!