Algebraic & Geometric Topology

JSJ decompositions of quadratic Baumslag–Solitar groups

Juan Alonso

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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.

Article information

Algebr. Geom. Topol., Volume 12, Number 4 (2012), 2027-2047.

Received: 7 November 2011
Revised: 20 June 2012
Accepted: 29 June 2012
First available in Project Euclid: 19 December 2017

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Zentralblatt MATH identifier

Primary: 20E06: Free products, free products with amalgamation, Higman-Neumann- Neumann extensions, and generalizations 20E08: Groups acting on trees [See also 20F65] 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx]
Secondary: 57M60: Group actions in low dimensions

JSJ decomposition generalized Baumslag–Solitar groups graphs of groups


Alonso, Juan. JSJ decompositions of quadratic Baumslag–Solitar groups. Algebr. Geom. Topol. 12 (2012), no. 4, 2027--2047. doi:10.2140/agt.2012.12.2027.

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