Gersten’s conjecture and virtual compact specialness of one-relator groups. Proves Gersten's conjecture: every finitely generated one-relator group containing no Baumslag–Solitar subgroup $\mathrm{BS}(m,n)$, with $m,n\ne0$, is word-hyperbolic. It also proves that every word-hyperbolic one-relator group is virtually compact special.
released 2026-09-25 | 4 theorems · 35 lemmas · 51 proofs · 26,192 words |
PLAY LEVEL 1 »(pdf)
We prove Gersten's conjecture: every finitely generated one-relator group containing no subgroup isomorphic to a Baumslag–Solitar group $\mathop{\mathrm{BS}}\nolimits (m,n)$, for nonzero integers m, n, is word-hyperbolic.
released 2026-09-25 | 10 theorems · 87 lemmas · 135 proofs · 80,869 words |
PLAY LEVEL 2 »(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.