Algebraic & Geometric Topology

Splittings of non-finitely generated groups

Robin M Lassonde

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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.

Article information

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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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 20E08: Groups acting on trees [See also 20F65] 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx]

splitting intersection number


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.

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