Seifert fibre spaces and Poincaré duality groups
We show that a Poincaré duality group of formal dimension three which has a subgroup of finite index with infinite abelianization and containing a nontrivial abelian normal subgroup is the fundamental group of a closed 3-manifold which is Seifert fibred or admits a Sol-structure. (With some obvious exceptions these algebraic conditions are satisfied by the groups of all such manifolds.) We give a corresponding characterization for the groups of bounded Seifert fibre spaces.
Poincaré duality group of formal dimension three
fundamental group of a closed 3-manifold
scientific article; zbMATH DE number 3883215