Algebraic & Geometric Topology

Splittings of non-finitely generated groups

Robin M Lassonde

Full-text: Open access

Abstract

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

Source
Algebr. Geom. Topol., Volume 12, Number 1 (2012), 511-563.

Dates
Received: 27 May 2011
Revised: 14 October 2011
Accepted: 12 December 2011
First available in Project Euclid: 19 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513715349

Digital Object Identifier
doi:10.2140/agt.2012.12.511

Mathematical Reviews number (MathSciNet)
MR2916286

Zentralblatt MATH identifier
1282.20047

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

Keywords
splitting intersection number

Citation

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


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