Floer homology, group orderability, and taut foliations of hyperbolic 3manifolds
Abstract
This paper explores the conjecture that the following are equivalent for rational homology 3spheres: having leftorderable 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 300,000 hyperbolic rational homology 3spheres. 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 3manifold has a taut foliation.
 Publication:

arXiv eprints
 Pub Date:
 April 2019
 arXiv:
 arXiv:1904.04628
 Bibcode:
 2019arXiv190404628D
 Keywords:

 Mathematics  Geometric Topology;
 Mathematics  Group Theory
 EPrint:
 49 pages, 13 figures and tables