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Graph manifolds, left-orderability and amalgamation

Adam Clay, Tye Lidman and Liam Watson

Algebraic & Geometric Topology 13 (2013) 2347–2368
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.

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/