Floer homology, group orderability, and tautfoliations of hyperbolic 3–manifolds

Abstract

This paper explores the conjecture that the following are equivalent for irreducible rational homology [math] –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 [math] hyperbolic rational homology [math] –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 [math] –manifold has a taut foliation.

Topics & Concepts