Volume 22, issue 3 (2018)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Orderability and Dehn filling

Marc Culler and Nathan M Dunfield

Geometry & Topology 22 (2018) 1405–1457
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 π1(M) into PSL2 ˜, which we organize into an infinite graph in H1(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.

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