JSJ decompositions of quadratic Baumslag–Solitar groups

Alonso, Juan

doi:10.2140/agt.2012.12.2027

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JSJ decompositions of quadratic Baumslag–Solitar groups

Juan Alonso

Algebraic & Geometric Topology 12 (2012) 2027–2047

DOI: 10.2140/agt.2012.12.2027

Abstract

Generalized Baumslag–Solitar groups are defined as fundamental groups of graphs of groups with infinite cyclic vertex and edge groups. Forester [Geom. Topol. 6 (2002) 219-267] proved that in most cases the defining graphs are cyclic JSJ decompositions, in the sense of Rips and Sela. Here we extend Forester’s results to graphs of groups with vertex groups that can be either infinite cyclic or quadratically hanging surface groups.

Keywords

JSJ decomposition, generalized Baumslag–Solitar groups, graphs of groups

Mathematical Subject Classification 2010

Primary: 20E06, 20E08, 20F65

Secondary: 57M60

References

Publication

Received: 7 November 2011

Revised: 20 June 2012

Accepted: 29 June 2012

Published: 29 October 2012

Authors

Juan Alonso
Department of Mathematics Cornell University 310 Malott Hall Ithaca NY 14853 USA
http://www.math.cornell.edu/People/PhD/alonso.html

Volume 12, issue 4 (2012)