Authors: Robert P Kropholler, Ian J Leary and Ignat Soroko

Affiliations: Tufts (RPK), Southampton (IJL), Oklahoma (IS)

Previously, one of the authors constructed uncountable 
families of groups of type $FP$ and of $n$-dimensional
Poincar\'e duality groups for each $n\geq 4$.  We show
that the groups previously constructed comprise 
uncountably many quasi-isometry classes.  We deduce 
that for each $n\geq 4$ there are uncountably many 
quasi-isometry classes of acyclic $n$-manifolds 
admitting free cocompact properly discontinuous 
discrete group actions.