Groups whose word problems are not semilinear

Suppose that G is a finitely generated group and W is the formal language of words defining the identity in G. We prove that if G is a nilpotent group, the fundamental group of a finite volume hyperbolic three-manifold, or a right-angled Artin group whose graph lies in a certain infinite class, then W is not a multiple context free language

Uncountably many quasi-isometry classes of groups of type FPFP

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 strengthen these results by showing that these groups 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.Comment: Version 2: minor corrections made, theorems now numbered by sectio

Closure properties in the class of multiple context-free groups

We show that the class of groups with k-multiple context-free word problem is closed under graphs of groups with finite edge groups.ISSN:1869-610

Uncountably many quasi-isometry classes of groups of type <i>FP</i>

In an earlier paper, one of the authors constructed uncountable families of groups of type F P and of n-dimensional Poincaré duality groups for each n ≥ 4. We show that those groups com-prise uncountably many quasi-isometry classes. We deduce that for each n ≥ 4 there are uncountably many quasi-isometry classes of acyclic n-manifolds admitting free cocompact properly discontinuous discrete group actions.</p