# Graph manifolds, left-orderability and amalgamation

@article{Clay2013GraphML,
title={Graph manifolds, left-orderability and amalgamation},
author={Adam Clay and Tye Lidman and Liam Watson},
journal={Algebraic \& Geometric Topology},
year={2013},
volume={13},
pages={2347-2368}
}
• Published 2 June 2011
• Mathematics
• Algebraic & Geometric Topology
We show that every irreducible toroidal integer homology sphere graph manifold has a left-orderable fundamental group. This is established by way of a specialization of a result due to Bludov and Glass [Proc. Lond. Math. Soc. 99 (2009) 585–608] for the amalgamated products that arise, and in this setting work of Boyer, Rolfsen and Wiest [Ann. Inst. Fourier (Grenoble) 55 (2005) 243–288] may be applied. Our result then depends on known relations between the topology of Seifert fibred spaces and…
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