Splittings of Non-Finitely Generated Groups.

Splittings;Mathematics;Science;Mathematics

Lassonde, Robin M.Strauss, Martin ;

University of Michigan

关键词: Splittings;    Mathematics;    Science;    Mathematics;   

Others  :  https://deepblue.lib.umich.edu/bitstream/handle/2027.42/91432/lassonde_1.pdf?sequence=1&isAllowed=y

瑞士|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 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.