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2025-05-30 07:25:24

Virtual First Betti Number of GGS Groups
Andrew Ng
https://arxiv.org/abs/2505.23269 https://arxiv.org/pdf/2505.23269

Virtual First Betti Number of GGS Groups
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.