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.