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

Nathan M Dunfield

Geometry & Topology 24 (2020) 2075–2125

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 300000 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.

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