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2012 Splittings of non-finitely generated groups
Robin M Lassonde
Algebr. Geom. Topol. 12(1): 511-563 (2012). DOI: 10.2140/agt.2012.12.511

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.

Citation

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Robin M Lassonde. "Splittings of non-finitely generated groups." Algebr. Geom. Topol. 12 (1) 511 - 563, 2012. https://doi.org/10.2140/agt.2012.12.511

Information

Received: 27 May 2011; Revised: 14 October 2011; Accepted: 12 December 2011; Published: 2012
First available in Project Euclid: 19 December 2017

zbMATH: 1282.20047
MathSciNet: MR2916286
Digital Object Identifier: 10.2140/agt.2012.12.511

Subjects:
Primary: 20E08, 20F65

Rights: Copyright © 2012 Mathematical Sciences Publishers

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