Graph manifolds Z-homology 3-spheres and taut foliations

Michel Boileau; Steven Boyer

doi:10.1112/jtopol/jtv006

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arXiv · 1303.5264

Graph manifolds Z-homology 3-spheres and taut foliations

Michel Boileau·Steven Boyer

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Abstract

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.

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BibTeX RIS

Michel Boileau, Steven Boyer. 2013-03-21. Graph manifolds Z-homology 3-spheres and taut foliations. https://doi.org/10.1112/jtopol%2Fjtv006

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