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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 , with , is word-hyperbolic. It also proves that every word-hyperbolic one-relator group is virtually compact special.
Manuscripts in this family · 2
Baumslag-Solitar-free one-relator groups are hyperbolic
Sep 25, 2026·paper.pdf
We prove Gersten's conjecture: every finitely generated one-relator group containing no subgroup isomorphic to a Baumslag–Solitar group , for nonzero integers m, n, is word-hyperbolic.
Virtual compact specialness of hyperbolic one-relator groups
Sep 25, 2026·paper.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.