Volume 12, issue 1 (2012)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Splittings of non-finitely generated groups

Robin M Lassonde

Algebraic & Geometric Topology 12 (2012) 511–563
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.

Keywords
splitting, intersection number
Mathematical Subject Classification 2010
Primary: 20E08, 20F65
References
Publication
Received: 27 May 2011
Revised: 14 October 2011
Accepted: 12 December 2011
Published: 28 March 2012
Authors
Robin M Lassonde
Department of Mathematics
University of Michigan
Ann Arbor MI 48109
USA
http://www-personal.umich.edu/~lassonde/