JSJ decompositions of Quadratic Baumslag-Solitar groups

Details JSJ decompositions of Quadratic Baumslag-Solitar groups JSJ decompositions of Quadratic Baumslag-Solitar groups

2011-02-22

arxiv.org/abs/1102.4589v3

Mathematics

Group Theory

20 pages, 2 figures. Several corrections and improvements from referee's report. Imprtant changes in Definition 5.1, and the p

Scientific paper

Generalized Baumslag-Solitar groups are defined as fundamental groups of graphs of groups with infinite cyclic vertex and edge groups. Forester proved (in "On uniqueness of JSJ decompositions of finitely generated groups", Comment. Math. Helv. 78 (2003) pp 740-751) 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.

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