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 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 language | English (US) |
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Pages (from-to) | 1405-1457 |
Number of pages | 53 |
Journal | Geometry and Topology |
Volume | 22 |
Issue number | 3 |
DOIs | |
State | Published - Mar 16 2018 |
Keywords
- Dehn filling
- Orderable groups
ASJC Scopus subject areas
- Geometry and Topology