Splittings of non-finitely generated groups

Lassonde, Robin M¹

¹Department of Mathematics, University of Michigan, Ann Arbor MI 48109, USA

Algebraic and Geometric Topology, Tome 12 (2012) no. 1, pp. 511-563

Résumé

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 finiteness, 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, Swarup, Niblo and Sageev), 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.

Détail

DOI : 10.2140/agt.2012.12.511

Classification : 20E08, 20F65
Keywords: splitting, intersection number

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