Geometry & Topology

Orderability and Dehn filling

Marc Culler and Nathan M Dunfield

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

Article information

Source
Geom. Topol., Volume 22, Number 3 (2018), 1405-1457.

Dates
Received: 12 February 2016
Revised: 2 March 2017
Accepted: 15 April 2017
First available in Project Euclid: 31 March 2018

Permanent link to this document
https://projecteuclid.org/euclid.gt/1522461619

Digital Object Identifier
doi:10.2140/gt.2018.22.1405

Mathematical Reviews number (MathSciNet)
MR3780437

Zentralblatt MATH identifier
06864259

Subjects
Primary: 57M60: Group actions in low dimensions
Secondary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45} 57M05: Fundamental group, presentations, free differential calculus 20F60: Ordered groups [See mainly 06F15]

Keywords
orderable groups Dehn filling

Citation

Culler, Marc; Dunfield, Nathan M. Orderability and Dehn filling. Geom. Topol. 22 (2018), no. 3, 1405--1457. doi:10.2140/gt.2018.22.1405. https://projecteuclid.org/euclid.gt/1522461619


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