Orderability and Dehn filling

Culler, Marc¹ ; Dunfield, Nathan²

¹ Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, IL, United States
² Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL, United States

Geometry & topology, Tome 22 (2018) no. 3, pp. 1405-1457.

Résumé

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 ${\pi }_1\left(M\right)$ into $\widetilde{{PSL}_2ℝ}$, which we organize into an infinite graph in $H^1\left(\partial M;ℝ\right)$ 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.

Détail

DOI : 10.2140/gt.2018.22.1405

Classification : 57M60, 57M25, 57M05, 20F60
Keywords: orderable groups, Dehn filling

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