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Splittings of generalized Baumslag–Solitar groups

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Abstract

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.

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  1. Mathematics Department, University of Oklahoma, Norman, OK, 73019, USA

    Max Forester

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  1. Max Forester
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Correspondence to Max Forester.

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Forester, M. Splittings of generalized Baumslag–Solitar groups. Geom Dedicata 121, 43–59 (2006). https://doi.org/10.1007/s10711-006-9085-9

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  • DOI: https://doi.org/10.1007/s10711-006-9085-9

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