# Orderability and Dehn filling

@article{Culler2016OrderabilityAD,
title={Orderability and Dehn filling},
author={M. Culler and N. Dunfield},
journal={arXiv: Geometric Topology},
year={2016}
}
• Published 2016
• Mathematics
• arXiv: Geometric Topology
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 $\widetilde… Expand #### Figures from this paper Floer homology, group orderability, and taut foliations of hyperbolic 3–manifolds This paper explores the conjecture that the following are equivalent for rational homology 3-spheres: having left-orderable fundamental group, having non-minimal Heegaard Floer homology, andExpand Promoting circular-orderability to left-orderability • Mathematics • 2019 Motivated by recent activity in low-dimensional topology, we provide a new criterion for left-orderability of a group under the assumption that the group is circularly-orderable: A group$G$isExpand Azumaya Algebras and Canonical Components • Mathematics • 2017 Let$M$be a compact 3-manifold and$\Gamma=\pi_1(M)$. Work of Thurston and Culler--Shalen established the$\mathrm{SL}_2(\mathbb{C})$character variety$X(\Gamma)$as fundamental tool in the studyExpand Left-orderability for surgeries on twisted torus knots We show that the fundamental group of the$3$-manifold obtained by$\frac{p}{q}$-surgery along the$(n-2)$-twisted$(3,3m+2)$-torus knot, with$n,m \ge 1$, is not left-orderable if$\frac{p}{q} \geExpand
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