| In this dissertation, we calculate Sigma-invariants for cocompact actions of finitely generated groups on locally finite trees. Such an action G ↷ T corresponds to a graph of groups decomposition of G over finitely many subgroups. Moreover, for reasons to be explained, the actions we study all have non-finitely generated point stabilizers.;These invariants were introduced by Bieri, Neumann, and Strebel in 1987 as invariants of finitely generated groups. Bieri and Geoghegan later extended the theory to isometric actions by finitely generated groups on proper CAT(0) metric spaces. In both cases, the invariants provide information about finiteness properties of certain subgroups of the group in question, as well as providing other details about the structure of the group.;The dissertation is broken into two parts, which correspond to two distinct approaches to calculating invariants. In Part I we find a condition which, when satisfied, guarantees that the Sigma-invariants consist of at most a single point. In Part II, we discuss a method for calculating Sigma-invariants which exploits the relationship between Bass-Serre theory and covering space theory and is more generally applicable than the case of Part I. We provide some examples of the use of this method. |
