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

Nathan M. Dunfield

doi:10.2140/gt.2020.24.2075

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arXiv · 1904.04628

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

Nathan M. Dunfield

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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.

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BibTeX RIS

Nathan M. Dunfield. 2019-04-09. Floer homology, group orderability, and taut foliations of hyperbolic 3-manifolds. https://doi.org/10.2140/gt.2020.24.2075

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