Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 12, Number 1 (2012), 511-563.
Splittings of non-finitely generated groups
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.
Algebr. Geom. Topol., Volume 12, Number 1 (2012), 511-563.
Received: 27 May 2011
Revised: 14 October 2011
Accepted: 12 December 2011
First available in Project Euclid: 19 December 2017
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Lassonde, Robin M. Splittings of non-finitely generated groups. Algebr. Geom. Topol. 12 (2012), no. 1, 511--563. doi:10.2140/agt.2012.12.511. https://projecteuclid.org/euclid.agt/1513715349