L-spaces, taut foliations, and graph manifolds

  title={L-spaces, taut foliations, and graph manifolds},
  author={Jonathan Hanselman and Jacob Rasmussen and Sarah Dean Rasmussen and Liam Watson},
  journal={Compositio Mathematica},
  pages={604 - 612}
If $Y$ is a closed orientable graph manifold, we show that $Y$ admits a coorientable taut foliation if and only if $Y$ is not an L-space. Combined with previous work of Boyer and Clay, this implies that $Y$ is an L-space if and only if $\unicode[STIX]{x1D70B}_{1}(Y)$ is not left-orderable. 
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