Strebel infinite-index subgroup theorem
= Strebel infinite-index subgroup theorem
{c}
{title2=$[G:H]=\infty\Longrightarrow\operatorname{cd}_{\mathbb Z}H<\dim G$}
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.