OpenAI research collection · 2 manuscripts · Source checked 2026-10-19
Proves Gersten's conjecture: every finitely generated one-relator group containing no Baumslag–Solitar subgroup BS(m,n), with m,n\ne0, is word-hyperbolic. It also proves that every word-hyperbolic one-relator group is virtually compact special.
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We prove Gersten's conjecture: every finitely generated one-relator group containing no subgroup isomorphic to a Baumslag–Solitar group \mathop{BS}\nolimits (m,n), for nonzero integers m, n, is word-hyperbolic.
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We prove that every word-hyperbolic one-relator group is virtually compact special. Combined with the work of Kielak–Linton, this resolves Wise's virtual free-by-cyclic conjecture for hyperbolic one-relator groups: every such group is virtually free-by-cyclic, with the free kernel allowed to have infinite rank.
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