|
|||||
|
|
|
|
|
|
|
|
|
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/ | |
|
