Strebel infinite-index subgroup theorem ($[G:H]=\infty ⟹{\mathrm{cd}}_{\mathbb{Z}}H<\dim G$)

An infinite-index subgroup of an integral dimension-$d$ Poincare duality group has integral cohomological dimension at most $d-1$. No finiteness assumption on the subgroup is needed for this inequality. In dimension three it places every infinite-index subgroup in cohomological dimension at most two.