Graph manifolds Z-homology 3-spheres and taut foliations

Abstract

We show that a graph manifold which is a Z-homology 3-sphere not homeomorphic to either the 3-sphere or the Poincaré homology 3-sphere admits a horizontal foliation. This combines with known results to show that the conditions of not being an L-space, of having a left-orderable fundamental group, and of admitting a co-oriented taut foliation, are equivalent for graph manifold Z-homology 3-spheres.

16 pages

References in corpus (3)

• Algebraic functions and closed braids
• A note on cabling and L-space surgeries
• On L-spaces and left-orderable fundamental groups

Cited by in corpus (8)

• Bordered Floer homology and existence of incompressible tori in homology spheres
• A calculus for bordered Floer homology
• Toroidal homology spheres and SU(2)-representations
• Slope detection, foliations in graph manifolds, and L-spaces
• On lattice cohomology and left-orderability
• Taut foliations, braid positivity, and unknot detection
• Taut foliations, left-orderability, and cyclic branched covers
• Left-orderable, non-L-space surgeries on knots