Splittings of Non-Finitely Generated Groups.

Abstract

In geometric group theory one uses group actions on spaces to gain information about groups. One natural space to use is the Cayley graph of a group. The Cayley graph arguments that one encounters tend to require local niteness, and hence finite generation of the group. In this paper, I take the theory of intersection numbers of splittings of finitely generated groups (as developed by Scott, Scott-Swarup, and Niblo-Sageev-Scott-Swarup), and rework it to remove finite generation assumptions. I show that when working with splittings, instead of using the Cayley graph, one can use Bass-Serre trees.Ph.D.MathematicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/91432/1/lassonde_1.pd