Gersten’s conjecture and virtual compact specialness of one-relator groups

What OpenAI claims

Proves Gersten's conjecture: every finitely generated one-relator group containing no Baumslag–Solitar subgroup BS(m,n), with m,n ≠ 0, is word-hyperbolic. It also proves that every word-hyperbolic one-relator group is virtually compact special.

Papers (2)

1. Baumslag-Solitar-free one-relator groups are hyperbolic

   25 September 2026 · Preprint, not peer reviewed · PDF

   We prove Gersten's conjecture: every finitely generated one-relator group containing no subgroup isomorphic to a Baumslag–Solitar group BS (m,n), for nonzero integers m, n, is word-hyperbolic.

2. Virtual compact specialness of hyperbolic one-relator groups

   25 September 2026 · Preprint, not peer reviewed · PDF

   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.

Status

Preprint. The papers have not been independently reviewed. Treat the result as OpenAI's claim until other mathematicians have checked it. If a video exists, it illustrates the statement; it is not the proof.