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}
}
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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  • S. Boyer, Ying Hu
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    Transactions of the American Mathematical Society
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We study the left-orderability of the fundamental groups of cyclic branched covers of links which admit co-oriented taut foliations. In particular we do this for cyclic branched covers of fibred
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