Orderability and dehn filling

Marc Culler, Nathan M. Dunfield

Research output: Contribution to journalArticlepeer-review


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 PSL2ℝ, which we organize into an infinite graph in H1(∂M;ℝ) 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.

Original languageEnglish (US)
Pages (from-to)1405-1457
Number of pages53
JournalGeometry and Topology
Issue number3
StatePublished - Mar 16 2018


  • Dehn filling
  • Orderable groups

ASJC Scopus subject areas

  • Geometry and Topology


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