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2018 Orderability and Dehn filling
Marc Culler, Nathan M Dunfield
Geom. Topol. 22(3): 1405-1457 (2018). DOI: 10.2140/gt.2018.22.1405

Abstract

Motivated by conjectures relating group orderability, Floer homology and taut foliations, we discuss a systematic and broadly applicable technique for constructing left-orders on the fundamental groups of rational homology 3 –spheres. Specifically, for a compact 3 –manifold M with torus boundary, we give several criteria which imply that whole intervals of Dehn fillings of M have left-orderable fundamental groups. Our technique uses certain representations from π 1 ( M ) into PSL 2 ˜ , which we organize into an infinite graph in H 1 ( M ; ) called the translation extension locus. We include many plots of such loci which inform the proofs of our main results and suggest interesting avenues for future research.

Citation

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Marc Culler. Nathan M Dunfield. "Orderability and Dehn filling." Geom. Topol. 22 (3) 1405 - 1457, 2018. https://doi.org/10.2140/gt.2018.22.1405

Information

Received: 12 February 2016; Revised: 2 March 2017; Accepted: 15 April 2017; Published: 2018
First available in Project Euclid: 31 March 2018

zbMATH: 06864259
MathSciNet: MR3780437
Digital Object Identifier: 10.2140/gt.2018.22.1405

Subjects:
Primary: 57M60
Secondary: 20F60, 57M05, 57M25

Rights: Copyright © 2018 Mathematical Sciences Publishers

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Vol.22 • No. 3 • 2018
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