Floer homology, group orderability, and taut foliations of hyperbolic 3-manifolds
arXiv:1904.04628 · doi:10.2140/gt.2020.24.2075
Abstract
This paper explores the conjecture that the following are equivalent for rational homology 3-spheres: having left-orderable fundamental group, having non-minimal Heegaard Floer homology, and admitting a co-orientable taut foliation. In particular, it adds further evidence in favor of this conjecture by studying these three properties for more than 300,000 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.
49 pages, 13 figures and tables; V2: corrected typos, to appear in Geometry and Topology
References in corpus (1)
Cited by in corpus (8)
- Constrained knots in lens spaces
- Thin links and Conway spheres
- Census L-space knots are braid positive, except for one that is not
- L-spaces, taut foliations and the Whitehead link
- A unified Casson-Lin invariant for the real forms of SL(2)
- Two curious strongly invertible L-space knots
- Taut foliations, left-orders, and pseudo-Anosov mapping tori
- Zippers