Graph manifolds, left-orderability and amalgamation

Clay, Adam¹ ; Lidman, Tye² ; Watson, Liam³

¹CIRGET, Université du Québec à Montréal, Case postale 8888, Succursale centre-ville, Montréal QC H3C 3P8, Canada
²Department of Mathematics, University of Texas at Austin, 1 University Station, Austin, TX 78712, USA
³Department of Mathematics, UCLA, 520 Portola Plaza, Los Angeles, CA 90095, USA

Algebraic and Geometric Topology, Tome 13 (2013) no. 4, pp. 2347-2368

Résumé

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.

Détail

DOI : 10.2140/agt.2013.13.2347

Classification : 06F15, 20F60, 57M05
Keywords: graph manifolds, left-orderable groups, L–spaces, integer homology sphere, fundamental group

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