Orderability and Dehn filling

摘要

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 pi(1) (M) into (PSL2R) over tilde, which we organize into an infinite graph in H-1 (partial derivative 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.