Campinas

We will discuss some recent results with Martin Bridson about 
Sidki's construction X(G). In particular, if G is a finitely presented
group then X(G) is a finitely presented group. We will discuss as well the
result that if G has polynomial isoperimetric function and the maximal
metabelian quotient of G is virtually nilpotent then X(G) has polynomial
isoperimetric function. Part of the arguments we will use have homological
nature.

 One of the applications of the study of assymptotics of
homology groups in residually free groups of type FP_m is the calculation
of their analytic betti numbers in dimension up to m.