Graph manifold Z-homology 3-spheres and taut foliations

Michel Boileau (1) , Steven Boyer (2)

1 I2M - Institut de Mathématiques de Marseille
2 DMS - Département de Mathématiques et de statistique [UdeM- Montréal]

We show that a graph manifold which is a Z-homology 3-sphere not homeomorphic to either the 3-sphere or the Poincar\'e 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.

Mots clés: HOLOMORPHIC DISKS; ESSENTIAL LAMINATIONS; SPACE SURGERIES; FLOER HOMOLOGY; DEHN SURGERY; INVARIANTS; CIRCLE; HOMEOMORPHISMS; 3-MANIFOLDS; TRANSVERSE

Domaines: Topologie géométrique [math.GT]

Michel Boileau, Steven Boyer. Graph manifold Z-homology 3-spheres and taut foliations. Journal of topology, 2015, 8 (2), pp.571-585. ⟨10.1112/jtopol/jtv006⟩. ⟨hal-01302045⟩