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math.GR2026
A note on normal generation and the first -betti number
Sam P. Fisher, Yash Lodha
In , Osin and Thom conjectured that the first -Betti number of a torsion-free discrete group is bounded above by the normal rank of the group minus one. The conjectur…
math.GR2026
On the top-dimensional -Betti number of residually poly- groups
Sam P. Fisher, Pablo Sánchez-Peralta
Let be a residually poly- group of finite type. We prove that admits a poly- quotient with kernel satisfying $\mathrm{cd}_{\mathbb Q}(N) < \mathbb…