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Orderability and Dehn
filling
Marc Culler and Nathan M Dunfield |
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Geometry & Topology 22 (2018) 1405–1457
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Abstract |
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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 –spheres. Specifically, for a compact –manifold with torus boundary, we give several criteria which imply that whole intervals of Dehn fillings of have left-orderable fundamental groups. Our technique uses certain representations from into , which we organize into an infinite graph in 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. |
Keywords
orderable groups, Dehn filling
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Mathematical Subject Classification 2010
Primary: 57M60
Secondary: 57M25, 57M05, 20F60
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References |
Publication
Received: 12 February 2016
Revised: 2 March 2017
Accepted: 15 April 2017
Published: 16 March 2018
Proposed: Cameron Gordon
Seconded: András I. Stipsicz, Ciprian Manolescu
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Authors |
| Marc Culler | |
| Department of Mathematics,
Statistics and Computer Science University of Illinois at Chicago Chicago, IL United States |
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| http://math.uic.edu/~culler | |
| Nathan M Dunfield | |
| Department of Mathematics University of Illinois at Urbana-Champaign Urbana, IL United States |
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| http://dunfield.info | |
