Splittings of non-finitely generated groups

Lassonde, Robin M

doi:10.2140/agt.2012.12.511

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Splittings of non-finitely generated groups

Robin M Lassonde

Algebraic & Geometric Topology 12 (2012) 511–563

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.

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/

Volume 12, issue 1 (2012)