Graph manifolds, left-orderability and amalgamation

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.

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Keywords

graph manifolds, left-orderable groups, L–spaces, integer homology sphere, fundamental group

Mathematical Subject Classification 2010

Primary: 06F15, 20F60, 57M05

References

Publication

Received: 11 July 2011

Revised: 25 February 2013

Accepted: 14 March 2013

Published: 2 July 2013

Authors

Adam Clay
CIRGET Université du Québec à Montréal Case postale 8888, Succursale centre-ville Montréal QC H3C 3P8 Canada
http://thales.math.uqam.ca/~aclay/
Tye Lidman
Department of Mathematics University of Texas at Austin 1 University Station Austin, TX 78712 USA

Liam Watson
Department of Mathematics UCLA 520 Portola Plaza Los Angeles, CA 90095 USA
http://www.math.ucla.edu/~lwatson/

Volume 13, issue 4 (2013)

Adam Clay, Tye Lidman and Liam Watson

Abstract