Abstract
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 the orderability of their fundamental groups.
Citation
Adam Clay. Tye Lidman. Liam Watson. "Graph manifolds, left-orderability and amalgamation." Algebr. Geom. Topol. 13 (4) 2347 - 2368, 2013. https://doi.org/10.2140/agt.2013.13.2347
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