Exponential extensions of groups.

In this paper we study exponential extensions of G which are finitely generated G-subgroups of the [ t]-completion G[ t] of a given CSA-group G. Using BassSerre theory we prove that exponential extensions of G can be obtained from subgroups of G by free constructions of a special type. As an application of this technique we describe the cohomological and homological dimensions of finitely generated fully residually free groups and give an algorithm to compute them. [ABSTRACT FROM AUTHOR]