#### Volume 24, issue 4 (2020)

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Floer homology, group orderability, and taut foliations of hyperbolic $3$–manifolds

### Nathan M Dunfield

Geometry & Topology 24 (2020) 2075–2125
##### Abstract

This paper explores the conjecture that the following are equivalent for irreducible rational homology $3$–spheres: having left-orderable fundamental group, having nonminimal Heegaard Floer homology, and admitting a coorientable taut foliation. In particular, it adds further evidence in favor of this conjecture by studying these three properties for more than $300\phantom{\rule{0.3em}{0ex}}000$ hyperbolic rational homology $3$–spheres. New or much improved methods for studying each of these properties form the bulk of the paper, including a new combinatorial criterion, called a foliar orientation, for showing that a $3$–manifold has a taut foliation.

##### Keywords
Floer homology, orderable groups, taut foliations, hyperbolic $3$–manifolds
##### Mathematical Subject Classification 2010
Primary: 57M27
Secondary: 20F60, 20M05, 57M05, 57M50, 57R30, 57R58
##### Publication
Received: 9 April 2019
Accepted: 27 October 2019
Published: 10 November 2020
Proposed: Cameron Gordon
Seconded: Rob Kirby, Ian Agol
##### Authors
 Nathan M Dunfield Department of Mathematics University of Illinois at Urbana-Champaign Urbana, IL United States http://dunfield.info