Left-orderable fundamental groups and Dehn surgery on genus one 2–bridge knots

Hakamata, Ryoto; Teragaito, Masakazu

doi:10.2140/agt.2014.14.2125

Cited by 12 publications

(1 citation statement)

References 21 publications

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“…We prove Theorems 1.2 and 1.4 by studying representations of 3-manifold groups into the nonlinear Lie group G = PSL 2 R. Using such representations to order 3-manifold groups goes back at least to [EHN], and has been exploited repeatedly of late to provide evidence for Conjecture 1.1. Closest to our results here, representations to G were used to obtain ordering results for Dehn surgeries on two-bridge knots in [HT,Tra2], as well as branched covers of two-bridge knots in [Hu,Tra1]. Indeed, some of the results on branched covers in [Hu,Tra1,Gor] can be viewed as special cases of both the statement and the proof of Theorem 1.4(a).…”

Section: Introductionmentioning

confidence: 89%

Orderability and Dehn filling

Culler

Dunfield

2018

Geom. Topol.

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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 π 1 (M ) into PSL 2 R, which we organize into an infinite graph in H 1 (∂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.

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