Geometriae Dedicata

, Volume 121, Issue 1, pp 43–59 | Cite as

Splittings of generalized Baumslag–Solitar groups

  • Max ForesterEmail author
Original Paper


We study the structure of generalized Baumslag–Solitar groups from the point of view of their (usually non-unique) splittings as fundamental groups of graphs of infinite cyclic groups. We find and characterize certain decompositions of smallest complexity (fully reduced decompositions) and give a simplified proof of the existence of deformations. We also prove a finiteness theorem and solve the isomorphism problem for generalized Baumslag–Solitar groups with no non-trivial integral moduli.


Baumslag–Solitar group G-tree Graph of groups Deformation Slide move Modular homomorphism 

Mathematics Subject Classifications (2000)

20E08 20F10 20E34 


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Copyright information

© Springer Science+Business Media B.V. 2006

Authors and Affiliations

  1. 1.Mathematics DepartmentUniversity of OklahomaNormanUSA

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