Volume 22, issue 3 (2018)

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Orderability and Dehn filling

Marc Culler and Nathan M Dunfield

Geometry & Topology 22 (2018) 1405–1457

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 π1(M) into PSL2 ˜, which we organize into an infinite graph in H1(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.

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orderable groups, Dehn filling
Mathematical Subject Classification 2010
Primary: 57M60
Secondary: 57M25, 57M05, 20F60
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
Marc Culler
Department of Mathematics, Statistics and Computer Science
University of Illinois at Chicago
Chicago, IL
United States
Nathan M Dunfield
Department of Mathematics
University of Illinois at Urbana-Champaign
Urbana, IL
United States