Virtual First Betti Number of GGS Groups
Group Theory
2025-05-30 v1
Abstract
We observe a criterion for groups to have vanishing virtual first Betti number and use it to give infinitely many examples of torsion-free, finitely generated, residually finite groups which aren't virtually diffuse. This answers a question raised by Kionke and Raimbault.
Cite
@article{arxiv.2505.23269,
title = {Virtual First Betti Number of GGS Groups},
author = {Andrew Ng},
journal= {arXiv preprint arXiv:2505.23269},
year = {2025}
}