Orderability and Dehn filling

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 $\tilde{{PSL}_{2} ℝ}$ , which we organize into an infinite graph in $H^{1} (\partial M; ℝ)$ 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.

PDF Access Denied

We have not been able to recognize your IP address 34.229.63.28 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recommendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

Keywords

orderable groups, Dehn filling

Mathematical Subject Classification 2010

Primary: 57M60

Secondary: 57M25, 57M05, 20F60

References

Publication

Received: 12 February 2016

Revised: 2 March 2017

Accepted: 15 April 2017

Published: 16 March 2018

Proposed: Cameron Gordon

Seconded: András I. Stipsicz, Ciprian Manolescu

Authors

Marc Culler
Department of Mathematics, Statistics and Computer Science University of Illinois at Chicago Chicago, IL United States
http://math.uic.edu/~culler
Nathan M Dunfield
Department of Mathematics University of Illinois at Urbana-Champaign Urbana, IL United States
http://dunfield.info

Volume 22, issue 3 (2018)

Marc Culler and Nathan M Dunfield

Abstract