• Corpus ID: 119272202

Slope detection, foliations in graph manifolds, and L-spaces

  title={Slope detection, foliations in graph manifolds, and L-spaces},
  author={Steven D. Boyer and Adam Clay},
  journal={arXiv: Geometric Topology},
  • S. Boyer, A. Clay
  • Published 8 October 2015
  • Mathematics
  • arXiv: Geometric Topology
A graph manifold rational homology $3$-sphere $W$ with a left-orderable fundamental group admits a co-oriented taut foliation, though it is unknown whether it admits a smooth co-oriented taut foliation. In this paper we extend the gluing theorem of arXiv:1401.7726 to graph manifold rational homology solid tori and use this to show that there are smooth foliations on the pieces of $W$ which come close to matching up on its JSJ tori. This is applied to prove that a graph manifold with left… 

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  • A. ClayD. Rolfsen
  • Mathematics
    Mathematical Proceedings of the Cambridge Philosophical Society
  • 2011
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