A group G is said to be of type FPoo if the ZG-module Z admits a projective resolution (Pi) of finite type (i.e., with each Pi finitely generated). If G is finitely presented, this is equivalent by Wall [5, 6] to the existence of an Eilenberg-Mac Lane complex K(G, 1) of finite type (i.e., with finitely many cells in every dimension). Up to now, all known torsion-free groups of type FPoo have ha...

A recent result of Bestvina and Brady [1], Theorem 8.7, shows that one of two outstanding questions has a negative answer: either there exists a group of cohomological dimension 2 and geometric dimension 3 (a counterexample to the Eilenberg-Ganea Conjecture [4]), or there exists a nonaspherical subcomplex of an aspherical 2-complex (a counterexample to the Whitehead Conjecture [11]). More preci...