Uncountably many quasi-isometric torsion-free groups

2025/11/18 by Vankov, Vladimir
Mathematics · #Geometric and Algebraic Topology #Advanced Operator Algebra Research #Homotopy and Cohomology in Algebraic Topology

paper · doi:10.48550/arxiv.2511.14277

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.

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