Splittings of Non-Finitely Generated Groups.

[摘要] In geometric group theory one uses group actions on spaces to gain informationabout groups. One natural space to use is the Cayley graph of a group. The Cayleygraph arguments that one encounters tend to require local niteness, and hence finitegeneration of the group. In this paper, I take the theory of intersection numbersof splittings of finitely generated groups (as developed by Scott, Scott-Swarup, andNiblo-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 canuse Bass-Serre trees.

[发布机构] University of Michigan

[效力级别] Mathematics

[关键词] Splittings;Mathematics;Science;Mathematics