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

Dunfield, Nathan M¹

¹ Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL, United States

Geometry & topology, Tome 24 (2020) no. 4, pp. 2075-2125.

Résumé

This paper explores the conjecture that the following are equivalent for irreducible rational homology $3$–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 $300000$ 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.

Détail

DOI : 10.2140/gt.2020.24.2075

Classification : 57M27, 20F60, 20M05, 57M05, 57M50, 57R30, 57R58
Keywords: Floer homology, orderable groups, taut foliations, hyperbolic $3$–manifolds

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