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Floer homology, group
orderability, and taut foliations of hyperbolic
$3$–manifolds
Nathan M Dunfield |
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Geometry & Topology 24 (2020) 2075–2125
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Abstract |
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This paper explores the conjecture that the following are equivalent for irreducible rational homology –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 hyperbolic rational homology –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 –manifold has a taut foliation. |
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Keywords
Floer homology, orderable groups, taut foliations,
hyperbolic $3$–manifolds
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Mathematical Subject Classification 2010
Primary: 57M27
Secondary: 20F60, 20M05, 57M05, 57M50, 57R30, 57R58
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References |
Publication
Received: 9 April 2019
Accepted: 27 October 2019
Published: 10 November 2020
Proposed: Cameron Gordon
Seconded: Rob Kirby, Ian Agol
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Authors |
| Nathan M Dunfield | |
| Department of Mathematics University of Illinois at Urbana-Champaign Urbana, IL United States |
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| http://dunfield.info | |
